List of Publications:
  1. An hp-Local discontinuous Galerkin Method for Some Quasi-linear Elliptic Boundary Value Problems of Non-monotone Type, Math. Comp. (accepted) (with Thirupathi Gudi and Neela Nataraj).
  2. On Approximation Theorems for Controllability of Non-linear Parabolic Problems, IMA J. Math. Control Info. (to appear) (with Mohan C Joshi and Anil Kumar).
  3. A qualocation method for Burger's equation, J. Comp. Math. Appl. (Accepted) (with Pritam S. Mantri and Neela Nataraj).
  4. Finite volume element method for second order hyperbolic equations, Intnl. J. Numer. Anal. Modelling (to appear) (with Sarvesh Kumar and Neela Nataraj).
  5. Discontinuos Galerkin Methods for Quasilinear Elliptic Problems on Nonmonotone Type, SIAM J. Numer Anal. 45 (2007), pp. 163-192 (with T. Gudi).
  6. Sliding Motion of Discontinuous Dynamical Systems Described by Semi-Implicit Index One Differential Algebraic Equations, 61 (2006), pp. 4722-4731, Chemical Engineering Science (with Kannan M. Moudgalya and Jyoti Agarwal).
  7. Linearized Backward Euler Method for the Equations of Motion Arising on the Oldroyd Model, SIAM J. Numer. Anal. 44 (2006), pp. 804-825 (with Jin Yun Yuan and Pedro D. Damazio).
  8. Numerical methods for the extended Fisher-Kolmogorov Equation, International J. Numer. Anal. and Modeling, 6 (2006), pp. 186-210 (with P. Dhanumjaya).
  9. Semidiscrete finite element Galerkin approximation to the equations of motion arising in the Oldroyd model, IMA J. Numer. Anal. 44 (2006), pp. 804-825 (with Jin Yun Yuan).
  10. Semidiscrete quolocation method for the Stefan problem’ Industrial Mathematics, Eds. Mohan C. Joshi, Amiya K. Pani and Sanjeev V. Sabnis, Narosa Publ. House, New Delhi (2006), pp. 105-120 (with L. Jones Doss).
  11. Equivalent dynamic solution of an industrial HDPE slurry reactor, ESCAPE-16/PSE-2006, Gramisch-Partenkirchen (2006 ), pp. 9-13 (with S. Nigam and K. M. Moudgalya).
  12. A quolocation method for unidimensional single phase Stefan problem, IMA J. Numer. Anal. 25 (2005), pp. 139-159 (with L. Jones Doss).
  13. Finite Element Approximation to a Class of Viscoelastic Problems with Short Memory under Conditions of Friction, Dynamics of Continuous, Discrete and Impulsive Systems, Ser B. 12 (2005), 360-380. (with Pradeepa Nair).
  14. Orthogonal cubic spline collocation method for the extended Fisher-Kolmogorov equation, Journal of Computational and Applied Mathematics , 174 (2005), pp. 101-117 (with P. Dhanumjaya).
  15. Finite element method for the extended Fisher-Kolmogorov (EFK) equation, Differential Equations and Dynamical Systems, Ed. D. Bhaguna, Narosa Publ. House, New Delhi (2005) (with P. Dhanumjaya).
  16. A nonlinear gas-liquid systems in the sliding motion, Differential Equations and Dynamical Systems, Ed. D. Bhaguna, Narosa Publ. House, New Delhi (2005) (with J. Agarwal and Kannan M. Moudgalya).
  17. A second order splitting lumped mass finite element method for the Rosenau equation, Differential Equations and Dynamical Systems, 12 (2004), pp. 331-351 (with Sang K. Chung).
  18. Sliding motion and stability of a class of discontinuous dynamical systems, Nonlinear Dynamics, 37 (2004), pp. 151-168 (with Jyoti Agarwal and Kannan M. Moudgalya).
  19. Higher order fully discrete scheme combined with H1-Galerkin mixed finite element method for semilinear reaction-diffusion equations, J. applied Mathematics and Computing, 15 (2004), pp. 1-28 (with S. Arul Veda Manickam and Kannan M. Moudgalya).
  20. An H1-Galerkin mixed method for second order hyperbolic equations, International J. Numer. Anal and Modeling, 1 (2004), pp. 111-130 (with Rajen K. Sinha and Ajaya K. Otta).
  21. Sliding motion of discontinuous dynamical systems described by differential algebraic equa- tions, Proceedings of the 2002 American Control Conference, Omni Press (2003), pp. 795-800 (with Jyoti Agarwal and Kannan M. Moudgalya).
  22. Semi-discrete finite element method for a class of visco- elastic problems with long memory under condition of friction, Proceeding of Hyp2002: Ninth International Conference on Hyperbolic Problems: Theory, Numerics and Applications, Springer Verlag (2203), pp. 745-754 (with Pradeepa Nair).
  23. The effect of spatial quadrature on the semidiscrete finite element Galerkin method for a strongly damped wave equation, Number Funct. Anal and Optimiz. 24(2003), no. 3-4, pp.311-325 (with Rajen K. Sinha and Sang K. Chung).
  24. Finite element methods for parabolic variational inequalities with a Volterra term, Numer Funct. anal & Optimize. 24(2003), pp. 107-127 (with Pradeepa Nair).
  25. An H1-Galerkin mixed finite element method for an evolution equation with a positive type memory term, SIAM J. Numer. Anal. 40 (2002), pp. 1475-1490 (with Graeme Fairweather).
  26. Control of higher index DAE system through a linear control law, Proceedings of the 2002 American Control Conference, Anchorage, Alaska, Omni Press (2002), pp. 465-470 (with Prashant Vora and Kannan M. Moudgalya).
  27. An efficient integration algorithm for a class of discontinuous dynamical systems in sliding motion, Proceedings of the 2002 American Control Conference, Anchorage, Alaska, Omni Press (2002), pp. 689-703 (with Jyoti Agrawal and Kannan M. Moudgalya)
  28. Finite element approximation to an evolutionary variational inequality with a Volterra term, Proceeding of the First International Conference on IndustrialMathematics in the Indian Sub- Continent, (Eds. A.H. Siddiqi and M. Ko˜cvara), Kluwer Academic Press, London (2002), pp. 317-338 (with Pradeepa Nair).
  29. H1-Galerkin mixed finite element methods for parabolic integro-differential equations, IMA J. Numer. Anal. 22 (2002), pp. 231-252 (with Graeme Fairweather).
  30. Numerical methods for the Rosenau equation, Applicable Analysis, 77 (2001), pp. 351-369 (with Sang K. Chung).
  31. Finite element approximation with quadrature to a time dependent parabolic integro-differential equations with non smooth initial data, J. Integral Equations and Appl.13 (2001), pp. 35-72 (with Rajen K. Sinha).
  32. Mixed finite element method for the strongly damped wave equation, Numer. Meth. PDE, 17 (2001), pp.105–119 (with Jin Yun Yuan).
  33. Error estimates for semidiscrete Galerkin method for time dependent parabolic integro-differential equations with non smooth data, CALCOLO: A Quarterly on Numerical Analysis and Theory of Computation, Springer Verlag Publ., 37 (2000), pp. 181-205 (with Rajen K. Sinha).
  34. A qualocation method for parabolic partial differential equations, IMA J. Numer. Anal. 19 (1999), pp. 473-495.
  35. The effect of spatial quadrature on finite element Galerkin approximation to a hyperbolic integro-differential equations, Numer. Funct. Anal. & Optimz. , 19 (1998), pp. 1129-1153. (with Rajen K. Sinha).
  36. A second order splitting combined with cubic spline orthogonal collocation method for the Rosenau equation, Numer. Meth. PDE. 14 (1998), pp. 695-716. (with Arul Veda Manickam and Sang K. Chung).
  37. On the backward Euler method for time dependent parabolic integro-differential equations with non smooth initial data, J. Integral Equations and Appl. 10 (1998), pp. 219-249. (with Rajen K. Sinha).
  38. Quadrature based finite element approximation to time dependent parabolic equations with non smooth initial data, CALCOLO: A Quarterly on Numerical Analysis and Theory of Computation, 35 (1998), pp. 225–248, Springer Verlag Publ. (with Rajen K. Sinha).
  39. A qualocation method for hyperbolic integro-differential equations, in the Proceedings of 4th SIAMInternational Conference on Mathematical and Numerical Aspects ofWave Propagation (June 1-5, 1998- Colorado School of Mines, Colorado), Ed. J. A. De Santo, SIAM Publication, Philadelphia, 1998, pp.723-726. (with Rajen K. Sinha).
  40. An H1-Galerkin mixed finite element method for the second order wave equations, in the Proceedings of 4th SIAM International Conference on Mathematical and Numerical Aspects of Wave Propagation (June 1-5, 1998- Colorado School of Mines, Colorado), Ed. J. A. De Santo, SIAM Publication, Philadelphia, 1998, pp.648-651.
  41. An H1-Galerkin mixed finite element method combined with the modified method of char- acteristics for incompressible miscible displacement problems in porous media, Differential Equations and Dynamical Systems 6 (1998), pp. 77-85. (with M. A. Mohammed Ali).
  42. An H1-Galerkin mixed finite element method for parabolic partial differential equations, SIAM J. Numer. Anal. 35 (1998), pp. 712-727.
  43. A second order splitting combined with cubic spline orthogonal collocation method for the Kuramoto- Sivashinsky equation, Computers & Mathematics with Applications, 35 (1998), pp. 5-25 (with Arul Veda Manickam and Kannan M. Moudgalya).
  44. A qualocation method for a second order semilinear two-point boundary value problem, Functional Analysis With Current Applications in Science, Technology and Industry, (Eds. M. Brokate and A. H. Siddiqi), Pitman Research Notes in Mathematics, Dec.’ 97, pp. 128-144. (with L. Jones T. Doss).
  45. Mixed Finite Element Methods for Compressible Miscible Displacement Problems in Reservoir Studies, Functional Analysis With Current Applications in Science, Technology and Industry, (Eds. M. Brokate and A. H. Siddiqi), Pitman Research Notes in Mathematics, Dec.’97 , pp. 332-352. (with M. A. Mohammed Ali).
  46. A priori L2-error estimates for a Stefan-type problem in one space dimension, Numer. Meth. PDEs., 13 (1997), pp.393-416. (with L. Jones T. Doss and S. Padhy).
  47. Convergence of finite difference method for the generalized solutions of Sobolev equations, J. Korean Math. Soc., 34 (1997), pp. 515-532. (with S. K. Chung, and M. G. Park).
  48. Finite element Galerkin method for the ‘good’ Boussinesq equation, Nonlinear Analysis: TMA, 29 (1997), pp. 937-956.(with Haritha Saranga).
  49. Weak solutions of integro-differential and functional differential equations, Differential Equations and Dynamical Systems 4 (1996), 411-422. (with T. Sengadir).
  50. Finite element methods with numerical quadrature for parabolic integro-differential equations, SIAM J. Numer. Anal., 33 (1996), pp. 1084-1105. (with Todd E. Peterson).
  51. Negative norm estimates and super convergence results for parabolic integro-differential equa- tions, J. Integral Equations and Appl., 8 (1996), pp. 65-98. (with Rajen K. Sinha).
  52. A Leray Schauder type theorem and its applications to neutral functional differential equations, Nonlinear Analysis TMA, 28 (1997), pp. 701-720. (with T. Sengadir and D. V. Pai).
  53. On the convergence of finite difference schemes for generalized solutions of Sobolev equations, J. Korean Math. Soc., 32 (1995), pp. 815-834. (with S. K. Chung).
  54. On super convergence results and negative norm estimates for a unidimensional single phase Stefan problem, Numer. Functional Anal. & Opt., 16 (1995), pp. 153-175. (with L. Jones T. Doss).
  55. Topological Transversality: applications to second order integro-differential and functional differential equations, Bull. Austral. Maths. Soc. 49 (1994), 251-264. (with T. Sengadir).
  56. A finite element method for a diffusion problem with constrained energy and nonlinear bound- ary conditions, J. Austral. Math. Soc. Ser B, 35 (1993), pp. 87-102.
  57. Numerical methods for hyperbolic and parabolic integro-differential equations, J. Integral Equations & Applications, 4 (1992), pp. 533-584 (with V. Thom´ee and L.B. Wahlbin).
  58. Finite element methods for identification of parameters in parabolic problems, CMA Proceedings of Mini-Conference on Inverse Problems in Partial Differential Equations, Australian National University, Canberra (August 23-25, 1990). A.K. Pani and R.S. Anderssen (eds.), CMA Proceedings, 31(1992), pp. 208-221 (with R.S. Anderssen).
  59. A priori error estimates for finite element Galerkin approximations to a free boundary problem in polymer technology, CMA Proceedings of Mini-Conference on Free and Moving Boundary and Diffusion Problems, Australian National University, Canberra (June 14-16, 1990), R.S. Anderssen, J.M. Hill and A.K. Pani (eds.), CMA Proceedings, 30 (1992), pp. 142-153 (with R.S. Anderssen).
  60. A finite element method for a single-phase semilinear Stefan problem in one space dimension, Numer. Funct. Anal. & Optimiz., 12 (1991), pp. 153-171 (with P.C. Das).
  61. A priori error estimates for a single-phase quasilinear Stefan problem in one space dimension, IMA J. Numer. Anal., 11 (1991), pp. 377-392 (with P.C. Das).
  62. A finite element Galerkin method for a unidimensional single-phase nonlinear Stefan problem with Dirichlet boundary conditions, IMA J. Numer. Anal., 11 (1991), pp. 99-113 (with P.C. Das).
  63. A finite element approximation to a unidimensional nonlinear ablation problem, Proceeding of 6th International Conference on ‘Numerical Methods in Thermal Problems’, Swansea 1989, R. W. Lewis (ed.), Peneridge Press (1990), pp. 101-107.
  64. Finite element approximation to a single phase quasilinear Stefan problem, Proceedings of International Colloquium on Free Boundary Problems : Theory and Applications. Isree/ Bavaria (West Germany) 1987, K.H. Hoffman and J. Sprekels (eds.), Pitman Research Notes in Mathematics Vol. 186, Longman Scientific & Technical Publ. (1990), pp. 582-588 (with P.C. Das).
  65. Rothe’s method to semilinear hyperbolic integro-differential equations, J. Appl. Math. & Stoch. Anal., 3 (1990), pp. 245-252 (with D. Bhaguna and V. Raghavendra).
  66. A priori error estimates in H1 and H2-norms for Galerkin approximations to a single phase nonlinear Stefan problem in one space dimension, IMA J. Numer. Anal., 9 (1989), pp. 213- 229 (with P.C. Das).
  67. An H1-Galerkin method for a Stefan problem with a quasilinear parabolic equation in non- divergence form, Internatl. J. Math. & Math. Sci., 10 (1987), pp. 35-360 (with P.C. Das).
  68. A method of interpolation of scattered data to a regular grid, Proceedings of National Space Science Symposium, Guwahati University (Feb. 19-22), 1986 (with P.K. Mishra).
  69. An H1-Galerkin method for quasilinear parabolic differential equations, Proceedings of International Conference on Methods of Functional Analysis in Approximation Theory, IIT, Bombay 1985. C.A. Micchelli, D.V. Pai and B.V. Limaye (eds.) International Series of Numerical Mathematics 76, Birkh¨auser Verlag Publ. (1986), 356-370 (with P.C. Das).
  70. C0-interior-penalty Galerkin method for slightly compressible miscible displacement in porous media, Proceedings of International Conference on Nonlinear Mechanics, Sanghai (China), Chein Wei Zang (ed.), Science Press, Sanghai (1985), 1186-1191 (with P.C. Das).