Computing

, Volume 90, Issue 3–4, pp 89–111 | Cite as

Finite central difference/finite element approximations for parabolic integro-differential equations

Article

Abstract

We study the numerical solution of an initial-boundary value problem for parabolic integro-differential equation with a weakly singular kernel. The main purpose of this paper is to construct and analyze stable and high order scheme to efficiently solve the integro-differential equation. The equation is discretized in time by the finite central difference and in space by the finite element method. We prove that the full discretization is unconditionally stable and the numerical solution converges to the exact one with order Ot2 + hl). A numerical example demonstrates the theoretical results.

Keywords

Parabolic integro-differential equation Finite element method Stability Error estimate 

Mathematics Subject Classification (2000)

65M06 65M12 65M22 65M60 35M13 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.College of Mathematics and Computer ScienceHunan Normal UniversityChangshaPeople’s Republic of China

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