Search

Abstract: Integro-differential equations of Volterra type arise, naturally, in many applications such as for instance heat conduction in materials with memory, diffusion in polymers and diffusion in porous media. The aim of this paper is to study a finite difference discretization of the mentioned integro-differential equations. Second convergence order with respect to the norm is established which means that the discretization proposed is supraconvergent in finite difference methods language. As the finite difference method can be seen as a piecewise linear finite element method combined with special quadrature formulas, our result establishes the supercloseness of the gradient in the finite element language. Numerical results illustrating the discussed theoretical results are included. [Copyright &y& Elsevier]

Abstract: In this paper we study numerical methods for integro-differential initial boundary value problems that arise, naturally, in many applications such as heat conduction in materials with memory, diffusion in polymers and diffusion in porous media. Here, we propose finite difference methods to compute approximations for the continuous solutions of such problems. We analyze stability and study convergence for those methods. Supraconvergent estimates are obtained. As such methods can be seen as lumped mass methods, our supraconvergent result corresponds to a superconvergent property in the context of finite element methods. Numerical results illustrating the theoretical results are included. [ABSTRACT FROM AUTHOR]