LIST OF PUBLICATIONS
1. A numerical method for solving mildly non-linear elliptic problems over irregular regions, Indian J. Pure and Applied Maths., Vol.7, no.2, pp. 212-223, 1976 (with P.C. Jain).
2. Dynamic programming solutions of mildly non-linear elliptic problems over irregular regions, International J. Computer Math., Section B, Vol. 5, pp. 231-239, 1976 (with P.C. Jain)
3. Invariant imbedding approach for the solution of minimal surface equation, J. Math. Anal. and Applications, Vol. 61, no. 3, pp. 543-557, 1977 (with P.C.Jain)
4. Invariant imbedding method for the solution of coupled Burger's equations, J. Math. Anal. and Applications, Vol. 72, no. 1, pp. 1-16, 1979 (with P.C. Jain)
5. Iterative techniques for non-linear boundary control problems, In Optimizing Methods in Statistics, edited by J.S. Rustagi, Proceedings of an International Conference, Academic Press, pp. 289-300, 1979 (with P.C. Jain and Labib Iskandar)
6. A numerical technique for solving nonlinear elliptic problems, Indian J. Pure and Applied Maths., Vol. 11, no. 1, pp. 20-32, 1980 (with P.C. Jain)
7. Numerical solution of a quasilinear parabolic problem, Proc. Indian Acad. Sci., (Mathematical Sciences), Vol. 89, no. 1, pp. 67-33, 1980 (with P.C. Jain)
8. Symmetric marching technique for the discretized Poisson equation, Applied Mathematics and Computation, Vol. 12, no. 3, pp.197-198, 1983 (with K.K. Bharadwaj and R. Sankar)
9. Symmetric marching technique for the efficient solution of discretized Poisson equation on non-rectangular regions, Numerical Methods in Laminar and Turbulent Flow, edited by C. Taylor and B. Schrefler, Proceedings of an International Conference, Pineridge Press, pp. 1215-1228, 1981 (with K.K. Bharadwaj)
10. Symmetric marching technique for the Poisson equation. I. Dirichlet boundary conditions, Applied Mathematics and Computation, Vol. 15, no. 2, pp. 137-150, 1984 (with K.K. Bharadwaj and R. Sankar)
11. Symmetric marching technique for the Poisson equation. II. mixed boundary condition.Applied Mathematics and Computation, Vol. 15, no.2, pp.151-164, 1984 (with K.K. Bharadwaj and R. Sankar)
12. Symmetric marching technique for the numerical solution of nonseparable elliptic equations, Applied Mathematics and Computation, Vol. 14, no. 2, pp. 197-206, 1984 (with K.K. Bharadwaj)
13. Symmetric marching technique and elliptic equation with variable coefficients involving mixed partial derivatives, Applied Mathematics and Computation, Vol. 15, no. 4, pp. 315-324, 1984 (with K.K. Bharadwaj)
14. Fast elliptic solvers - An overview, Applied Mathematics and Computation, Vol. 14, no. 4, pp. 331-356.
15. Numerical solution of singular boundary value problems by invariant imbedding, J. Computational Physics, Vol. 55, no. 2, pp. 268-277, 1984 (with K.S. Raman)
16. Discrete invariant imbedding for the numerical solution of boundary-value problems over infinite intervals, Applied Mathematics and Computation, Vol. 15, no. 4, pp. 305-314, 1984 (with K.S. Raman)
17. On fast direct methods for solving elliptic equations over nonrectangular regions, Applied Mathematics and Computation, Vol. 16, no. 1, pp. 1-17, 1985 (with K.K. Bharadwaj)
18. Numerical solution of singular boundary value problems via Chebyshev polynomials and invariant imbedding, Technical Report, Dept. of Maths., IIT. Kanpur, 1984 (with K.S. Raman)
19. Cubic spline and invariant imbedding for solving singular two-point boundary value problems, J. Math. Anal. and Applications, Vol. 112, no. 1, pp. 22-35, 1985 (with K.S. Raman)
20. Cubic spline solutions of boundary value problems over infinite intervals, J. Computational and Appl. Mathematics, Vol. 15, pp. 283-291, 1986 (with K.S. Raman)
21. Numerical solution of Cauchy singular integral equations via initial value methods, Applied Mathematics and Computation, Vol. 18, no. 3, pp. 211-222, 1986.
22. Invariant imbedding method for the solution of elliptic equations with boundary singularities, Presented at the Vth IMACS International Conference on Computer Methods for Partial Differential Equations, Lehigh University, Bethelhem, U.S.A., June 19-22, 1984.
23. A numerical scheme for solving singular perturbation problems by invariant imbedding, Technical Report, Dept. of Maths., IIT Kanpur, 1986 (with Y.N. Reddy).
24. The method of inner boundary conditions: A new approach for solving singular perturbation problems, J. Computational Physics, Vol. 62, pp. 349-360, 1986 (with Y.N. Reddy).
25. Discrete invariant imbedding for singular boundary value problems with a regular singularity, Applied Math. & Computation, Vol. 22, no. 4, pp. 291-308, 1987 (with K.S. Raman)
26. Numerical solution of singular perturbation problem using cubic splines, Technical Report, Dept. of Mathematics, IIT Kanpur (with Y.N. Reddy)
27. Modified fourth order finite difference methods for singular boundary value problems I: linear case, Technical Report, Dept. of Mathematics, IIT Kanpur, 1985 (with K.S. Raman)
28. Modified fourth order finite difference methods for singular boundary value problems II: nonlinear case, Technical Report, Dept. of Mathematics, IIT Kanpur, 1985 (with K.S. Raman)
29. A computational method for solving singular perturbation problems using fourth order finite difference, Comm. In Appl. Numer. Methods, Vol. 2, pp. 609-615, 1986 (with Y.N. Reddy)
30. Numerical solution of singular perturbation problems by terminal boundary value technique, J. Optimiz. Theory and Applications, Vol. 52, no. 2, pp. 243-254, 1987 (with Y.N. Reddy)
31. Numerical treatment of singularly perturbed two-point boundary value problems, Applied Mathematics and Computation, Vol. 21, no. 2, pp. 93-110, 1987 (with Y.N. Reddy)
32. Approximate method for the numerical solution of singular perturbation problems, Applied Mathematics and Computation, Vol. 21, no. 3, pp. 185-200, 1987 (with Y.N. Reddy)
33. Numerical integration of a class of singular perturbation problems, J. Optimiz. Theory and Applications, Vol. 51, no. 3, pp. 441-452, 1986 (with Y.N. Reddy)
34. An asymptotic and numerical analysis of singular perturbation problems-A survey, Technical Report, Dept. of Mathematics, IIT Kanpur, 1987.
35. Numerical analysis- some problems and recent trends, Proceedings of an International Workshop on Engineering Software- Applications and Research, held during Jan. 21-25, 1985 at IIT Kanpur.
36. Numerical solution of singular perturbation problems via deviating arguments, Applied Mathematics and Computation, Vol. 21, no. 3, pp. 221-232, 1987 (with Y.N. Reddy)
37. An approximate method for solving a class of singular perturbation problems, J.Math. Anal. & Applic., Vol. 133, no. 2, pp. 306-323, 1988 (with Y.N. Reddy)
38. An initial value technique for a class of nonlinear singular perturbation problems, J. Optimiz. Theory and Applic., Vol. 53, no. 3, pp. 395-406, 1987 (with Y.N. Reddy)
39. A non-asymptotic method for singular perturbation problems, J. Optimiz. Theory and Applic., Vol. 55, no. 1, pp. 73-84, 1987 (with Y.N. Reddy)
40. A non-asymptotic method for general linear singular perturbation problems, J. Optimiz. Theory and Applic., Vol. 55, no. 2, pp. 257-270, 1987 (with Y.N. Reddy)
41. A boundary value method for a class of nonlinear singular perturbation problems, Comm. Appl. Numerical Methods, Vol. 4, pp. 587-594, 1988 (with Y.N.Reddy)
42. A boundary value technique to solve linear state regulator problems, j. Optimiz. Theory and Applic., Vol. 63, no. 1, pp. 91-107, 1989 (with A. Singh)
43. A cutting point technique for solving nonlinear state regulator problems, IMA J. of Math. Control and Information, Vol. 4, pp. 183-194, 1987 (with A. Singh)
44. A boundary value technique for solving singularly perturbed fixed end-point optimal control problems, Optimal Control Applications and Methods, Vol. 9, pp. 443-448, 1988 (with A. Singh)
45. Numerical Treatment of Stiff Linear Block-diagonal Systems of ODEs, Communicated for publication (with A. Singh)
46. On a linearization of nonlinear autonomous two-point boundary value problems, Communicated for publication (with A. Singh).
47. A numerical method for solving singularly perturbed systems of non linear two-point boundary value problems, Technical Report, Department of Mathematics, IIT, Kanpur (with A. Singh)
48. Estimate of boundary layer thickness for linear singularly perturbed two-point boundary value problems, J. Optimiz. Theory & Applic., Vol. 63, no. 1, pp .143-151, 1989 (with A. Singh)
49. Partial decoupling of slow and fast variables, J. Math. Anal. & Applic. Vol. 155, no. 1, pp. 46-54, 1991 (with A. Singh)
50. Numerical solution of singularly perturbed two-point boundary value problems - Some new approaches, Technical Report, Department of Mathematics, IIT Kanpur, 1989.
51. A modified version of Newtons iteration, International J. Comput. Math., Vol. 33, pp. 107-113, 1990 (with A. Singh)
52. A fourth order cubic spline method for initial value problems, Communicated for publication (with R.K. Bawa)
53. Cubic spline method for a class of nonlinear singularly perturbed boundary value problems, J. Optimiz. Theory and Applic., Vol. 76, no. 3, pp. 415-428, 1993 (with R.K. Bawa)
54. Numerical solution of singularly perturbed initial value problems using a fourth order cubic spline, Communicated for publication (with R.K. Bawa)
55. Third order variable mesh cubic spline method for singularly perturbed boundary value problems, Applied Mathematics & Computation, Vol. 59, no. 2-3, pp. 117-129, 1993 (with R.K. Bawa)
56. Third order variable mesh cubic spline method for nonlinear two-point singularly perturbed boundary value problems, J. Optimiz. Theory and Applic., Vol. 77, no. 2, pp. 439-449, 1993 (with R.K. Bawa)
57. Variable mesh difference scheme for singularly perturbed boundary value problems using splines, J. Optimiz. Theory and Applic., Vol. 90, no. 2, pp. 405-416, 1996 (with R.K. Bawa)
58. Existence of the new quadrant interlocking factorization for parallel solution of tridiagonal linear systems, International Journal of Computer Mathematics, Vol. 48, pp. 95-103, 1993 (with S.C. Rao)
59. On the existence of the new quadrant interlocking factorization for parallel solution of tridiagonal linear systems, International Journal of Computer Mathematics, Vol. 51, pp. 181-192, 1994 (with S. Chandrasekara Rao)
60. The alternating group explicit (AGE) method for singularly perturbed boundary value problems, Applied Mathematics & Computation, Vol. 68, pp. 125-142, 1995 (with A. Appaji Rao)
61. On modified alternating group explict (MAGE) method for singular perturbation problems, International Journal of Computer Mathematics, Vol. 51, pp. 239-249, 1994 (with A. Appaji Rao)
62. Parallel method for singularly perturbed boundary value problems, Parallel Algorithms and Applications, Vol. 8, pp. 121-131, 1995 (with A. Appaji Rao)
63. Parallel new group explicit method for solving tridiagonal systems, Submitted for publication (with A. Appaji Rao)
64. Parallel group explicit method for two dimensional parabolic equation, Parallel Computing, Vol. 23, pp. 649-666, 1997 (with A. Appaji Rao)
65. Parallel WDZ algorithm for parabolic equations with a small parameter, Submitted for publication (with A. Appaji Rao).
66. Parallel AGE algorithm for parabolic equations with a small parameter, Parallel Algorithms and Applications, Vol. 8, pp. 155-168, 1996 (with A. Appaji Rao)
67. Parallel discrete invariant imbedding algorithm for singular perturbation problems, International Journal of Computer Mathematics, Vol. 66, pp. 149-161, 1998 (with A. Appaji Rao)
68. Boundary element method for elliptic differential equation with a small parameter, Applied Mathematics & Computation, Vol. 80, pp. 1-13, 1995 (with K.Arumugam)
69. On fundamental solution in boundary element method for singular perturbation problems, Boundary Element Communications, Vol. 8, pp. 14-17, 1997 (with K. Arumuguam)
70. Boundary element method for singularly perturbed elliptic boundary value problems, J. Computational Physics, to appear (with K. Arumugam)
71. Parallel group explicit algorithms for nonlinear singular perturbation problems with variable mesh, Submitted for publication (with A. Appaji Rao)
72. On nonlinear singular perturbation problems of elliptic type using boundary element method, Submitted for publication (with K. Arumugam)
73. Performance analysis of AGE algorithm for singular perturbation problems, Parallel Algorithm & Applications, Vol. 10, pp. 315-318, 1997 (with A. Appaji Rao)
74. A parallel algorithm for banded linear systems, Parallel Algorithm & Applications, Vol. 14, pp. 235-252, 2000 (with S.C.Rao)
75. Variable mesh spline approximation method for solving singularly perturbed turning point problems having boundary layer(s), Computers and Mathematics with Applications, Vol. 42, no. 10-11, pp. 1439-1453, 2001 (with K.C. Patidar)
76. Numerical solution of singularly perturbed non linear two point boundary value problems by spline in compression, International Journal of Computer Mathematics, Vol. 79, no. 2, pp. 271-288, 2002 (with K.C. Patidar)
77. Spline techniques for the numerical solution of singular perturbation problems, J. Optimization Theory & Applications, Vol. 112, no. 3, pp. 574-594, 2002 (with K.C. Patidar)
78. Spline techniques for solving singularly perturbed non-linear problems on non-uniform grids, J. Optimization Theory & Applications, Vol. 114, no. 3, pp. 573-591, 2002 (with K.C. Patidar)
79. Spline approximation method for solving self-adjoint singular perutrbation problems on non-uniform grids, Journal of Computational Analysis and Applications, Vol. 5, no. 4, pp. 425-451, 2003 (with K.C. Patidar)
80. Variable mesh spline in compression for the numerical solution of singular perturbation problems, International J. Computer Mathematics, Vol. 80, no. 1, pp. 83-93, 2003 (with K.C. Patidar)
81. Exponentially fitted spline in compression for the numerical solution of singular perturbation problems, Computers and Mathematics with applications, Vol. 46, no. 5-6, pp. 751-767, 2003 (with K.C. Patidar)
82. Exponentially fitted spline approximation method for solving self-adjoint singular perturbation problems, International J. of Mathematics and Mathematical Sciences, Vol. 61, pp. 3873-3891 (with K.C. Patidar)
83. Variable mesh spline approximation method for solving singularly perturbed turning point problems having interior layer. To appear in Journal of computational methods in science and engineering (with K.C. Patidar)
84. Singularly perturbed problems in partial differential equations - a survey, Applied Mathematics and Computation, Vol. 134, no. 2-3, pp. 371-429, 2003 (with K.C. Patidar)
85. Numerical solution of singularly perturbed two point boundary value problems by spline in Compression, International journal of Computer Mathematics, Vol. 77, no. 2, pp. 263-284, 2001 (with K.C. Patidar)
86. Numerical solution of singularly perturbed two point boundary value problems by spline in tension, Applied Mathematics Computation, Vol. 131, no. 2-3, pp. 299-320, 2002 (with K.C. Patidar)
87. Tension spline for the solution of self-adjoint singular perturbation problems, International J. Computer Mathematics, Vol. 79, no. 7, pp. 849-865, 2002 (with K.C. Patidar)
88. Tension spline for the numerical solution of singularly perturbed non-linear boundary value problems, Computational and Applied Mathematics, Vol. 112, no. 3, pp. 717-742, 2002 (with K.C. Patidar)
89. A survey of numerical techniques for solving singularly perturbed ordinary differential equations, Applied Mathematics and Computation, Vol. 130, no. 2-3, pp. 457-510, 2002 (with K.C. Patidar)
90. Numerical analysis of boundary value problems for singularly perturbed differential difference equations with small shifts of mixed type, J. Optimization Theory & Applications, Vol. 115, pp. 145-163, 2002 (with K.K. Sharma)
91. Variable mesh spline approximation method for solving singularly perturbed turning point problems having layer, to appear in J. of Comp. methods in science and engineering (With K.C. Patidar)
92. Singularly perturbed problems in partial differential equations: a survey, Applied Mathematics and Computation, Vol. 134, no. 2-3, 371-429, 2003 (with K.C. Patidar)
93. Exponentially fitted spline in compression for the numerical solution of singular perturbation problems, Computers and Mathematics with Applications, Vol. 46, no. 5-6, pp. 751-767, 2003 (with K.C. Patidar)
94. Variable mesh spline in compression for the numerical solution of singular perturbation problems, International Journal of Computer Mathematics, Vol. 80, no. 1, pp. 83-93, 2003 (with K.C. Patidar)
95. Numerical Analysis of Non-Linear Boundary Value Problems for Singularly Perturbed Delay Differential Equations with Layer Behavior, Technical Report, IIT Kanpur, 2003 (with K.K. Sharma)
96. An ε-uniform fitted operator method for solving boundary value problems for singularly perturbed delay differential equations: Layer behavior, International J. of Computer Mathematics, Vol. 80, no. 10, pp. 1261-1276, 2003 (with K.K. Sharma).
97. Numerical analysis of boundary value problems for singularly Perturbed differential-Difference Equations: small shifts of mixed type with rapid oscillations, Communication in numerical methods in engineering, Vol. 20, pp. 167-182, 2004 (with K.K.Sharma)
98. ε-uniform fitted mesh method for singularly perturbed differential-difference equations: Mixed type of shifts with layer behavior, International J. of Computer Mathematics, Vol. 81, No. 1, PP. 49-62, 2004 (with K.K.Sharma)
99. Numerical Analysis of Singularly Perturbed Delay Differential Equations with layer behavior, Applied Mathematics and Computation, Vol. 157, no. 1, pp. 11-28, 2004 (with K.K. Sharma)
100. Parameter Uniform Numerical Method for a Singularly Perturbed Nonlinear Delay Differential Equation of Neutral Type, International J. of Computer Mathematics, Vol. 81, pp. 845-862, 2004 (with K.K. Sharma)
101. Cubic Spline for solving Singular Two-Point Boundary Value Problems, Applied Mathematics and Computation, Vol. 156, no. 1, pp. 249-259, 2004 (with Vivek Kumar)
102. Numerical Treatment for Singularly Perturbed Differential Difference Equations with negative shift, Nonlinear Analysis, Vol. 63, no. 5-7, pp. e1909-e1924, 2005 (with K.K Sharma)
103. Numerical Treatment of a Mathematical Model arising from a model of neuronal variability, Journal of Mathematical Analysis and Applications, Vol. 307, no. 2, pp. 606-627, 2005 (with K.K Sharma)
104. Numerical Treatment of Boundary-Value Problems for Second Order Singularly Perturbed Delay Differential Equations, Computational and Applied Mathematics, Vol. 24, no. 2, pp. 151-172, 2005 (with K.K. Sharma)
105. Numerical Solution of Singular Boundary Value Problems Via Chebyshev Polynomial and B-Spline, Applied Mathematics and Computation, Vol. 160, no. 3, pp. 851-863, 2005 (with Vivek Kumar)
106. Fitted Mesh B-spline Collocation method for solving Self-Adjoint Singularly Perturbed boundary value problems, Applied Mathematics and Computation, Vol. 161, no. 3, pp. 973-987, 2005(With Vivek Kumar)
107. Fitted Mesh B-spline method for solving a class of singular singularly perturbed boundary value problems, International Journal of Computer Mathematics, Vol. 82, no. 1, pp. 67-76, 2005(With Vivek Kumar)
108. A parameter-uniform implicit difference scheme for solving time-dependent Burgers' equations, Applied Mathematics and Computation, Vol. 170, no. 2, pp. 1365-1393, 2005 (With Kapil K. Sharma and Ashish Awasthi)
109. An ε-Uniform Convergent Method for a General Boundary-Value Problem for Singularly Perturbed Differential-Difference Equations: Small Shifts of Mixed type with Layer Behavior, Journal of Computational Methods in Science and Engineering, Vol. 6, no. 1-4, pp. 39-55, 2006 (with K.K. Sharma)
110. A Numerical Method Based on Finite Difference for Boundary Value Problems for Singularly Perturbed Delay Differential Equations, Accepted in Int. J. of Computer Mathematics (with K.K. Sharma)
111. Numerical Analysis of a Mathematical Model arising in Mathematical Modeling of Propagating Nerve Impulse in Nerve Fibers (Communicated)
112. B-Spline Method for solving Singular Two-point Boundary Value Problems over infinite intervals, Communicated, (With Vivek Kumar)
113. B-Spline Method for solving general Singularly Perturbed Bondary Value Problems using Fitted mesh, Computing letters, Vol. 2, no. 4, pp. 193-203, 2006 (With Vivek Kumar)
114. Parameter -Uniform Fitted Mesh Method for Singularly Perturbed Delay Differential Equations with Layer Behavior, Electronics Transactions on Numerical Analysis (ETNA), Vol. 23, pp. 180-201, 2006 (with K.K. Sharma)
115. An Exponentially Fitted Finite Difference Scheme for Solving Boundary-Value Problems for Singularly-Perturbed Differential-Difference Equations: Small Shifts of Mixed Type with Layer Behavior, J. Comput. Anal. Appl., Vol. 8, no. 2, pp. 151-171, 2006 (with K.K. Sharma)
116. Fitted Mesh B-Spline Collocation method for solving Singularly Perturbed Reaction-Diffusion Problems, J. of Concrete and Applicable Mathematics, NOVA Pub., Vol. 4, no. 3, pp. 349-365, 2006 (With Vivek Kumar)
117. ε-uniformly convergent fitted methods for the numerical solution of the problems arising from singularly perturbed general DDEs, Applied Mathematics and Computation, Vol. 182, no. 1, pp. 119-139, 2006 (with K.C. Patidar and K.K. Sharma)
118. ε-uniformly convergent fitted mesh finite difference methods for general singular perturbation problems, Applied Mathematics and Computation, Vol. 179, no. 1, pp. 248-266, 2006 (with K.C. Patidar)
119. ε-Uniformly convergent fitted methodsfor the numerical solution of problems arising from singularly perturbed general DDEs, Report Nr. UWC-MRR 2006/01, Univesity of the Western Cape, March 2006 (with K.C.Patidar and K.K. Sharma)
120. Variable mesh spline approximation method for solving singularly perturbed turning point problems having interior layer, Neural, Parallel and Scientific Computations, Vol. 18, no.2, pp.207-220,2010 (with K.C. Patidar)
121. A Parameter Uniform Difference Scheme for Singularly Perturbed Parabolic Problem in one Space Dimension, Applied Mathematics and Computation, Vol. 183, no. 1, pp. 42-60, 2006 (with Ashish Awasthi)
122. Numerical Method Based on Crank-Nicolson Scheme For Burgers' Equation, Applied Mathematics and Computation", Vol. 182, no. 2, pp. 1430-1442, 2006 (with Ashish Awasthi)
123. A High Resolution Total Variation Diminishing Scheme for Hyperbolic Conservation Law and Related Problems, Applied Mathematics and Computation, Vol 175, no. 2, pp. 1556-1573, 2006 (with Ritesh Kumar)
124. Efficient High-Resolution Relaxation Schemes for Hyperbolic Systems of Conservation Laws, International Journal for Numerical Methods in Fluids, Vol 55, no. 5, pp. 483-507, 2007 ( with Ritesh Kumar)
125. B-spline method for a class of singular two-point boundary value problems using optimal grid, Applied Mathematics and Computation, Vol. 188, no. 2, pp. 1816-1831, 2007 (With Vivek Kumar)
126. Numerical methods on Shishkin mesh for singularly perturbed delay differential equations with a grid adaptation strategy, Applied Mathematics and Computation, Vol. 188, no. 2, pp. 1816-1831, 2007 (with V.P. Ramesh)
127. Hybrid method for numerical solution of singularly perturbed delay differential equations, Applied Mathematics and Computation, Vol. 187, no. 2, pp. 797-814, 2007 (with V.P. Ramesh)
128. Geometric mesh FDM for self adjoint singular perturbation boundary value problems, Applied Mathematics and Computation, Vol. 190, no. 2, pp. 1646-1656, 2007 (with Devendra Kumar)
129. A numerical method based on finite difference for boundary value problems for singularly perturbed delay differential equations, Applied Mathematics and Computation, Vol. 197, no. 1, pp. 692-707, 2008 (with Kapil K. Sharma)
130. A class of High resolution Shock Capturing Schemes for Hyperbolic Conservation Laws, Applied Mathematics and Computation, Vol. 195, pp. 110-126, 2008 (with Ritesh Kumar)
131. Crank-Nicolson Finite Difference Method Based on Midpoint Upwind Scheme on Non-Uniform Mesh For Time Dependent Singularly Perturbed Convection Diffusion Equations, International Journal of Computer Mathematics, Vol. 85, pp. 771-790, 2008 (with Ashish Awasthi)
132. A uniformly convergent B-spline collocation method on a nonuniform mesh for singularly perturbed one-dimensional time-dependent linear convection-diffusion problem, Journal of Computational and Appllied Mathematics, Vol. 220, pp. 271-289, 2008 (with Vikas Gupta and Ashish Awasthi)
133. Uniformly Convergent Numerical Method for Solving Modified Burgers' Equations on a Non-Uniform Mesh, Journal of Numerical Mathematics, Vol. 16, pp. 217-235, 2008 (with Ashish Awasthi)
134. Upwind and midpoint upwind difference methods for time dependent differential difference equations with layer behavior, Applied Mathematics and Computation, Vol. 202, no. 2, pp. 453-471, 2008 (with V.P. Ramesh)
135. B-Spline collocation method for a two parameter singularly perturbed convection-diffusion boundary value problems, Applied Mathematics and Computation, Vol. 201, pp. 504-513, 2008 (with Arjun Singh Yadaw)
136. Comparative study of singularly perturbed two point BVPs via: fitted mesh finite difference method, B-spline collocation method and finite element method, Applied Mathematics and Computation, Vol. 204, pp. 713-725, 2008 (with Arjun Singh Yadaw and Devendra Kumar)
137. A non-linear single step explicit scheme for non-linear two-point singularly perturbed boundary value problems via initial-value technique, Applied Mathematics and Computation, Vol. 202, pp. 738-746, 2008 (with Devendra Kumar)
138. Fitted mesh B-Spline collocation method for singularly perturbed differential-difference equations with small delay, Applied Mathematics and Computation, Vol. 204, pp. 90-98, 2008 (with Devendra Kumar)
139. Parameter-uniform fitted operator B-spline collocation method for self-adjoint singularly perturbed two-point boundary value problems, Electronic Transactions on Numerical Analysis, Vol. 30, pp. 346-358, 2008 (with Devendra Kumar)
140. Space-time Galerkin Least-Squares method for the one-dimensional advection-diffusion equation, International Journal of Computer Mathematics, First published online on 21st August 2008 (with Puneet Arora)
141. Composite High Resolution Localized Relaxation Scheme based on Upwinding for Hyperbolic Conservation Laws, International Journal for Numerical Methods in Fluids, Vol. 61, pp. 638-657, 2009 (with Ritesh Kumar)
142. Numerical solution of singularly perturbed convection-diffusion problem using parameter uniform B-spline collocation method, Journal of Mathematical Analysis and Applications, Vol. 355, pp. 439-452, 2009 (with Vikas Gupta)
143. An epsilon-uniform Ritz-Galerkin finite element Method for numerical solution of singularly perturbed delay differential equations, International journal of pure and applied Mathematics, Vol. 55, no. 2, pp. 257-265, 2009 (with Arjun Singh Yadaw)
144. A parameter-uniform Ritz-Galerkin finite element method for singularly perturbed delay differential equation with delay in convection term, International journal of pure and applied Mathematics, Vol. 57, no. 4, pp. 459-474, 2009 (with Arjun Singh Yadaw)
145. Parameter-uniform Ritz-Galerkin finite element method for two parameter singularly perturbed boundary value problems, International journal of pure and applied Mathematics, Vol. 55, no. 2, pp. 265-287, 2009 (with Arjun Singh Yadaw)
146. Initial value technique for singularly perturbed two point boundary value problems using an exponentially fitted finite difference scheme, Computers & Mathematics with Applications, Vol. 57, pp. 1147–1156 (2009) (with Devendra Kumar)
147. B-Spline collocation method for a singularly perturbed reaction– diffusion problem using artificial viscosity, International Journal of Computational Methods, Vol. 6, pp. 23-41, 2009 (with Puneet Arora)
148. B-spline collocation method for the singular-perturbation problem using artificial viscosity, Computer and Mathematics with Applications, Vol. 57, pp. 650-653, 2009 (with Puneet Arora)
149. Taylor-Galerkin B-Spline finite element method for the one-dimensional advection-diffusion equation, Numerical Methods for Partial Differential Equations, Published online (www.interscience.wiley.com), DOI 10.1002/num.20488 (with Puneet Arora)
150. Variable mesh finite difference method for self adjoint singularly perturbed two point boundary value problems, Journal of Computational Mathematics, Vol. 28, no. 5, pp.711-724,2010 (with Devendra Kumar)
151. A computational method for singularly perturbed nonlinear differential-difference equations with small delay, Applied Mathematical Modeling, Vol. 34, no. 9, pp.2584-2596, 2010 (with Devendra Kumar)
152. A parameter uniform B-spline collocation method for solving singularly perturbed turning point problem having twin boundary layers, International Journal of Computer Mathematics, Vol. 87,, pp. 3218-3235 (with Vikas Gupta)
153. A layer adaptive B-spline collocation method for singularly perturbed one-dimensional parabolic problem with a boundary turning point, Numerical Methods for Partial Differential Equations, DOI:10.1002/num.20574 (with Vikas Gupta)
154. The Midpoint Upwind Finite Difference Scheme for Time Dependent Singularly Perturbed Convection-Difusion Equations on Non-Uniform Mesh, Computational Methods in Engineering Science and Mechanics, Accepted for Publication,( with Ashish Awasthi)
155. Parameter Free Hybrid Numerical Method for Solving Modified Burgers' Equations on a Non-Uniform Mesh, (Communicated with Ashish Awasthi)
156. Efficiency of high order numerical schemes for solving differential difference equations on a priori adaptive shishkin mesh (communicated with V.P. Ramesh)
157. High order numerical scheme for Stein's model of neuronal variability without turning point (Communicated with V.P. Ramesh)
158. Parameter uniform numerical scheme for second order singularly perturbed differential-differential equations with layer behavior, Neural, Parallel, and Scientific Computations, Vol. 17, no. 2, pp. 101-122, 2009 ( with V.P. Ramesh)
159. Numerical algorithm for singularly perturbed delay differential equations with layer and oscillatory behavior, Neural, Parallel, and Scientific Computations, Vol. 19, no. 2, pp. 21-34, 2011 ( with V.P. Ramesh)
160. B-Spline collocation method for singularly perturbed differential-difference equations with small shifts having layer behavior (Communicated with Devendra Kumar)
161. Numerical solution of singularly perturbed two point boundary value problems by exponentially fitted finite difference scheme (Communicated with Devendra Kumar)
162. Numerical treatment of singularly perturbed delay differential equations using B-Spline collocation method on Shishkin mesh J. of Numerical Analysis, Industrial and Applied Mathematics, Vol. 7, no. 3-4, pp. 73-90,2012( with Devendra Kumar)
163. A parameter-uniform numerical method for time-dependent singularly perturbed differential-difference equations with small shifts, Applied Mathematical Modeling, Vol. 34, no.6, pp. 2805-2819, 2011 ( with Devendra Kumar)
164. Parameter-uniform solution of singularly perturbed boundary value problems having turning points (Communicated with Devendra Kumar)
165. A hybrid finite difference scheme with Shishkin mesh for solving singularly perturbed one-dimensional parabolic problem (Communicated with Vikas Gupta)
166. Qualitative analysis and numerical modelling of Burgers' equation via B-spline collocation method on an adaptive mesh (Communicated with Vikas Gupta)
167. A parameter robust hybrid finite difference scheme for singularly perturbed parabolic problem with two small parameters (Communicated with Vikas Gupta)
168. Numerical approximation of modified Burgers' equation via hybrid finite difference scheme on layer-adaptive mesh , Neural, Parallel, and Scientific Computations, Vol. 18, pp. 167-194, 2010 ( with Vikas Gupta)
169. Hybrid finite difference method for solving modified Burgers' and Burger-Huxley equations, Neural, Parallel, and Scientific Computations, Vol. 18, pp. 409-422, 2010 ( with Vikas Gupta)
170. B-spline collocation method for two parameter singularly perturbed two point boundary value problems via asymptotic expansion Appl. Math. Inf. Sci., Vol. 6, no. 1, pp. 29-33, 2012(with Arjun Singh Yadaw and Devendra Kumar)
171. Finite difference, finite element and B-Spline collocation methods applied to two parameter singularly perturbed boundary value problems, Journal of Numerical Analysis, Industrial and Applied Mathematics (JNAIAM), Vol. 5, no. 3-4,pp.163-180,2011 ( with Arjun Singh Yadaw)
172. Parameter-Uniform finite element method for two-parameter singularly perturbed parabolic reaction-diffusion problems International J. Computational Methods, Vol. 9, 2012, DOI: 10.1142/S0219876212500478 ( with Arjun Singh Yadaw)
173. B-spline collocation solution of self-adjoint singular perturbation problems by incorporation of artificial viscosity (Communicated with Puneet Arora)
174. B-Splines collocation method for solving singular perturbation problems using artificial viscosity Computers and Mathematics with Applications,Vol. 57, no.4,pp.650-663,2009 (with Puneet Arora)
175. Collocation method using artificial viscosity for solving stiff singularly perturbed turning point problem having twin boundary layers, Computers and Mathematics with Applications, Vol. 61, pp. 1595-1607, 2011 ( with Vikas Gupta and Puneet Arora)
176. Uniformly convergent fitted spline method for Multiple boundary turning point problems (Communicated with Puneet Arora)
177. A B-splines collocation solution of singularly perturbed delay differential equations of the convection-diffusion type using artificial viscosity (Communicated with Puneet Arora)
178. Collocation solution of singularly perturbed delay differential equations with shifts of mixed type (Communicated with Puneet Arora)
179. Design of a fitted collocation method for a convection-diffusion problem with two small parameters Neural, Parallel and Scientific Computing, Vol. 20,pp. 133-152,2012(with Puneet Arora)
180. Fitted collocation method for a singularly perturbed one-dimensional time-dependent linear convection-diffusion problem Proceedings od Dynamic Systems and Applications, Vol. 6,pp. 197-204,2012 (with Puneet Arora)
181. A brief survey on numerical methods for solving singularly perturbed problems, Applied Mathematics and Computation, Vol. 217, pp. 3641- 3716,2010 (with Vikas Gupta)
182. A singular perturbation approach to solve Burger-Huxley equation via hybrid finite difference scheme on layer adaptive mesh, Communications in Nonlinear Science and Numerical Simulations, Vol. 16, pp. 1825-1844, 2011 ( with Vikas Gupta)
183. An overview on the eigen value computation for matrices, Neural, Parallel, and Scientific Computations, Accepted for publication (with Ankit Gupta)
184. Analysis of fitted Spline in compression for convection diffusion problems with two small parameters, Neural, Parallel, and Scientific Computations, Accepted for publication (with Anuradha Jha)
185. Exponentially fitted cubic spline for two parameter singularly perturbed boundary value problems, Submitted for publication (with Anuradha Jha)
186. Cubic B-spline collocation method for numerical solution of generalized Black-Scholes equation, Submitted for publication (with Lokpati Tripathi and Alpesh Kumar)
187. Radial basis function Taylor-Collocation method for convection-diffusion problems, Submitted for publication( with Lokpati Tripathi & Alpesh Kumar)
188. A Robust Fitted Mesh Method for Singularly Perturbed Turning Point Problems for Differential Difference Equations, Submitted for publication( with Kapil K Sharma and Pratima Rai)