- Deepjyoti Goswami, A. K. Pani and Sangita Yadav (Accepted),
*Optimal L2 estimates for semidiscrete Galerkin methods for parabolic integro-differential equations with nonsmooth data,*Australian and New Zealand Industrial and Applied Mathematics Journal (2013). - S. Bajpai, N. Nataraj and A. K. Pani (Accepted),
*On a two-grid finite element scheme for the equations of motion arising in the Kelvin-Voigt model*, Adv. Comp. Math. (2013). - Amiya K. Pani, Ambit K.Pani, P. Damazio and J. Y. Yuan (Accepted),
*A modified nonlin- ear spectral Galerkin method for the equations of motion arising in the Kelvin-Voigt fluids,*Applicable Analysis, 2013. - Deepjyoti Goswami, A.K. Pani and Sangita Yadav (2013),
*Optimal error estimates of two mixed finite element methods for parabolic integro-difierential equations with nonsmooth initial data*, J.Sci. Comp.,56, 131-164. - * S. Yadav, A.K.Pani and E.J.Park (2013),
*Superconvergent discontinuous Galerkin methods for nonlinear elliptic equations,*Math. Comp., 82, pp. 1297-1335. - S. Bajpai, N. Nataraj and A. K. Pani (2013), On fully discrete finite element schemes for equa- tions of motion of Kelvin-Voigt fluids, Intl.J. Numer. Anal. Modelling, 10, pp.481507
- Sangita Yadav, Amiya K. Pani and Neela Nataraj (2013),
*Superconvergent Discontinuous Galerkin Methods for Linear Non-selfadjoint and Indefinite Elliptic Problems,*Journal of Scientific Computing, 54, 4576. - S. Bajpai, N. Nataraj, A. K. Pani, P. Damazio and J. Y. Yuan (2013), Semidiscrete Galerkin method for equations of motion arising in Kelvin-Voigt model of viscoelastic fluid ow, Numer.Meth. PDE., 29, 857-883.
- * Sajid Memon, Neela Nataraj and Amiya K. Pani (2012),
*An Aposteriori Error Analysis of a Mixed Finite Element Galerkin Approximation to Second Order Linear Parabolic Problems*SIAM J. Numer. Anal., 50, pp. 1367-1393. - P. Danumjaya and A.K. Pani (2012),
*Mixed finite element methods for a fourth order reaction difiusion equation,*Numer Meth PDE.,28, pp. 12271251. - Deepjyoti Goswami and A.K.Pani (2011),
*An Alternate Approach to Optimal L2-error anal- ysis of semidiscrete Galerkin methods for linear parabolic problems with nonsmooth initial data,*Numer. Funct. Anal. Optimz., 32, pp. 946-982. - D. Pradhan,S. Baskar, Neela Nataraj and A.K. Pani (2011), A
*Robin-type Non-Overlapping Domain Decomposition Procedure for Second Order Elliptic Problems*, Adv. Comput. Math. 34, pp. 339-368. - * Deepjyoti Goswami and A. K. Pani ( 2011 ), A
*priori error estimates for semidiscrete finite element approximations to equations of motion arising in Oldroyd fuids of order one,*International J. Numer. Anal and Modelling (IJNAM), 8, pp.324-352. - * A.K. Pani and Sangita Yadav (2011), An hp-local discontinuous Galerkin method for parabolic integro-differential equations, J. Sci. Comp. 46, pp.71-99.
- *A. K. Pani, G. Fairweather and R.I. Fernandes (2010), ADI
*Orthogonal Spline Collocation Methods for Parabolic Integro-Differential Equations*, IMA J Numer Anal. 30, pp. 248-276. - Nupur Gupta, Neela Nataraj and A.K. Pani (2010), On the
*optimal control problem of laser surface hardening,*Internl. J. Numer Anal. Model, 7, pp. 667-680. - Sarvesh Kumar,Neela Nataraj and A. K. Pani (2009),
*Discontinuous Galerkin finite volume methods for second order linear elliptic problems,*Numer. Meth. PDEs.25, pp.1402-1424. - * T. Gudi, Neela Nataraj and A. K. Pani (2009),
*On L*J. Comput. Appl. Math.228,pp.30-40.^{2}-Error Estimate for Non-Symmetric Interior Penalty Galerkin Approximation to Linear Elliptic Problems with Nonhomogeneous Dirichlet Data, - * T. Gudi, Neela Nataraj and A. K. Pani (2008), A
*mixed discontinuous Galerkin method for the biharmonic equation,*J. Scientific Computing. 37,pp.139-161. - A.K. Patel, A.K. Pani and Neela Nataraj (2008 ) A
*mortar element method for parabolic problems*, Numer. Meth. PDEs.24,pp.1460-1484. - * T. Gudi, Neela Nataraj and A. K. Pani (2008),
*hp-discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems,*Numer. Math.109, pp.233-268. - * A. K. Pani, Graeme Fairweather and Ryan Fernandes (2008),
*Alternate Direction Implicit Orthogonal Spline Collocation Methods for an Evolution Equation with a positive type memory term,*SIAM J. Numer. Anal.46, pp. 344-364. - D. Pradhan, A.K. Pani and Neela Nataraj ( 2008 ),
*An explicit/implicit Galerkin domain decomposition procedure for parabolic integro-difierential equations*,J Appl. Math. Comp.28, pp. 295-311. - * T. Gudi, Neela Natraj and A. K. Pani ( 2008 ),
*An hp-local discontinuous Galerkin method for some quasi-linear elliptic boundary value problems of non-monotone type ,*Math. Comp. 77, pp. 731-756. - Sarvesh Kumar, Neela Natraj and A. K. Pani (2008),
*Finite volume element method for second order hyperbolic equations,*Intnl.J . Numer. Anal and Modeling.5 , pp. 132-151. - Pritam Mantri, Neela Natraj and A.K. Pani (2008),
*A quolocation method for Burgers' equation,*J. Comp. Math. Appl. 213, pp. 1-13. - * Anil Kumar, M. C. Joshi and A. K. Pani (2007),
*On Approximation Theorems for Control- lability of Non-linear Parabolic Problems,*IMA J. Math. Control Info.24, pp.115-136. - * T. Gudi and A. K. Pani (2007),
*Discontinuos Galerkin Methods for Quasilinear Elliptic Problems on Nonmonotone*Type, SIAM J. Numer Anal. 45, pp. 163-192. - * J. Agarwal. Kannan Moudgalya and A. K. Pani (2006),
*Sliding Motion of Discontinuous Dynamical Systems Described by Semi-Implicit Index One Difierential Algebraic Equations,*61 , pp. 4722-4731, Chemical Engineering Science. - * A. K. Pani, Jin Yun Yuan and Pedro D. Damazio (2006),
*Linearized Backward Euler Method for the Equations of Motion Arising on the Oldroyd Model,*SIAM J. Numer. Anal. 44, pp. 804-825 . - P. Dhanumjaya and A. K. Pani ( 2006),
*Numerical methods for the extended Fisher-Kolmogorov Equation,*International J. Numer. Anal. and Modeling, 6, pp. 186-210. - * A. K. Pani and Jin Yun Yuan (2005),
*Semidiscrete finite element Galerkin approximation to the equations of motion arising in the Oldroyd model,*IMA J. Numer. Anal. 25, pp. 750-782. - Pradeepa Nair and A. K. Pani (2005),
*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: Appl. & Algorithm, 12, pp. 360-380. - * L Jones Doss and A. K. Pani (2005), A
*quolocation method for unidimensional single phase Stefan problem,*IMA J. Numer. Anal. 25, pp. 139-159 - P. Dhanumjaya and A. K. Pani (2005),
*Orthogonal cubic spline collocation method for the extended Fisher-Kolmogorov equation,*Journal of Computational and Applied Mathematics , 174, pp. 101-117. - A. K. Pani and Sang K. Chung (2004), A
*second order splitting lumped mass finite element method for the Rosenau equation, Differential Equations*and Dynamical Systems, 12 (2004), pp. 331-351. - * Jyoti Agarwal, Kannan M. Moudgalya and A. K. Pani (2004),
*Sliding motion and stability of a class of discontinuous dynamical systems,**Nonlinear Dynamics, 37, pp. 151-168.* - S. Arul Veda Manickam, Kannan M. Moudgalya and A. K. Pani (2004),
*Higher order fully dis- crete scheme combined with H1-Galerkin mixed finite element method for semilinear reaction- diffusion equations,*J. Applied Mathematics and Computing, 15, pp. 1-28. - Rajen K. Sinha, Ajay K. Otta and A. K. Pani (2004),
*An H*International J. Numer. Anal and Modeling, 1, pp. 111- 130.^{1}-Galerkin mixed method for second order hyperbolic equations, - Rajen K. Sinha, A. K. Pani and Sang K. Chung (2003),
*The effect of spatial quadrature on the semidiscrete finite element Galerkin method for a strongly damped wave equation,*Number Funct. Anal and Optimiz. 24, no. 3-4, pp. 311-325./li>

- Pradeepa Nair and A. K. Pani (2003),
*Finite element methods for parabolic variational in- equalities with a Volterra term,*Numer Funct. anal & Optimize. 24, pp. 107-127. - * A. K. Pani and Graeme Fairweather (2002),
*An H*SIAM J. Numer. Anal. 40, pp. 1475-1490.^{1}-Galerkin mixed finite element method for an evolution equation with a positive type memory term, - * A. K. Pani and Gareme Fairweather (2002), H
^{1}*Galerkin mixed finite element methods for parabolic integro-differential equations,*IMA J. Numer. Anal. 22, pp. 231{252. - * A. K. Pani and Sang K. Chung (2001),
*Numerical methods for the Rosenau equation,*Applicable Analysis, 77, pp. 351-369. - * Rajen K. Sinha and A. K. Pani (2001),
*Finite element approximation with quadrature to a time dependent parabolic integro-differential equations with non smooth initial data,*J. Integral Equations and Appl.13, pp. 35-72. - A. K. Pani and Jin Yun Yuan (2001),
*Mixed finite element method for the strongly damped wave equation,*Numer. Meth. PDE, 17, pp.105{119. - * Rajen K. Sinha and A. K. Pani (2000),
*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, pp. 181{205. - * A. K. Pani (1999), A
*qualocation method for parabolic partial differential equations,*IMA J. Numer. Anal. 19, pp. 473{495. - * Rajen K. Sinha and A. K. Pani (1998),
*The effect of spatial quadrature on finite element Galerkin approximation to a hyperbolic integro-differential equations,*Numer. Funct. Anal. & Optimz. , 19, pp. 1129{1153. - Arul Veda Manickam, Sang K. Chung and A. K. Pani (1998),
*A second order splitting com- bined with cubic spline orthogonal collocation method for the Rosenau equation,*Numer. Meth. PDE. 14, pp. 695{716. - * Rajen K. Sinha and A. K. Pani (1998),
*On the backward Euler method for time dependent parabolic integro-differential equations with non smooth initial data,*J. Integral Equations and Appl. 10, pp. 219{249. - * Rajen K. Sinha and A. K. Pani (1998),
*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, pp. 225{248, Springer Verlag Publ. - M. A. Mohammed Ali and A. K. Pani (1998),
*An H*Differential Equations and Dynamical Systems 6, pp. 77{85.^{1}-Galerkin mixed finite element method combined with the modified method of characteristics for incompressible miscible displacement problems in porous media, - * A. K. Pani (1998),
*An H*SIAM J. Numer. Anal. 35, pp. 712{727.^{1}-Galerkin mixed finite element method for parabolic partial dif- ferential equations, - Arul Veda Manickam, Kannan . Moudgalya and A. K. Pani (1998), A
*second order split- ting combined with cubic spline orthogonal collocation method for the Kuramoto- Sivashinsky equation,*Computers & Mathematics with Applications, 35, pp. 5{25. - * A. K. Pani, T Sengadir and D. V. Pai (1997),
*A Leray Schauder type theorem and its applications to neutral functional differential equations,*Nonlinear Analysis TMA, 28, pp. 701-720. - Jones T. Doss, S. Padhy and A. K. Pani (1997),
*A priori L2-error estimates for a Stefan-type problem in one space dimension,*Numer. Meth. PDEs., 13, pp. 393-416. - S. K. Chung, M. G. Park and A. K. Pani (1997),
*Convergence of finite difference method for the generalized solutions of Sobolev equations,*J. Korean Math. Soc., 34, pp. 515-532. - * Haritha Saranga and A. K. Pani (1997),
*Finite element Galerkin method for the `good' Boussinesq equation,*Nonlinear Analysis: TMA, 29, pp. 937-956. - T. Sengadir and A. K. Pani (1996), Weak solutions of integro-differential and functional differential equations, Differential Equations and Dynamical Systems 4, 411-422.
- * A.K. Pani and Todd E. Peterson (1996),
*Finite element methods with numerical quadrature for parabolic integro-differential equations,*SIAM J. Numer. Anal., 33, pp. 1084-1105 - Rajen K. Sinha and A. K. Pani (1996),
*Negative norm estimates and super convergence results for parabolic integro-differential equations,*J. Integral Equations and Appl., 8, pp. 65-98. - S. K. Chung and A. K. Pani (1995),
*On the convergence of finite difference schemes for generalized solutions of Sobolev equations,*J. Korean Math. Soc., 32, pp. 815-834. - L Jones T. Doss and A. K. Pani (1995),
*On super convergence results and negative norm estimates for a unidimensional single phase Stefan problem,*Numer. Functional Anal. & Opt., 16, pp. 153-175. - T. Sengadir and A. K. Pani (1994),
*Topological Transversality: applications to second order integro-differential and functional differential equations,*Bull. Austral. Maths. Soc. 49, 251-264. - A. K. Pani (1993),
*A finite element method for a diffusion problem with constrained energy and nonlinear boundary conditions,*J. Austral. Math. Soc. Ser B, 35, pp. 87-102. - * A. K. Pani, V. Thomee and L. B. Wahlbin (1992),
*Numerical methods for hyperbolic and parabolic integro-differential equations,*J. Integral Equations & Applications, 4, pp. 533-584. - A. K. Pani and P. C. Das (1991),
*A finite element method for a single-phase semilinear Stefan problem in one space dimension,*Numer. Funct. Anal. & Optimiz., 12 (1991), pp. 153-171.23 - * A. K. Pani and P. C. Das (1991),
*A priori error estimates for a single-phase quasilinear Stefan problem in one space dimension,*IMA J. Numer. Anal., 11, pp. 377-392. - * A. K. Pani and P. C. Das (1991), A
*finite element Galerkin method for a unidimensional single-phase nonlinear Stefan problem with Dirichlet boundary conditions*IMA J. Numer. Anal., 11, pp. 99-113. - D. Bhaguna, V. Raghavendra and A. K. Pani (1990),
*Rothe's method to semilinear hyperbolic integro-differential equations,*J. Appl. Math. & Stoch. Anal., 3, pp. 245-252. - * A. K. Pani and P. C. Das (1989), A
*priori error estimates in H*IMA J. Numer. Anal., 9, pp. 213-229.^{1}and H^{2}-norms for Galerkin approximations to a single phase nonlinear Stefan problem in one space dimension, - A. K. Pani and P. C. Das (1987), An
*H*Internatl. J. Math. & Math. Sci., 10, pp. 35-360.^{1}-Galerkin method for a Stefan problem with a quasilinear parabolic equation in non-divergence form,