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

Authors:
Wulan Li;Xu Da
Affiliations:
Hunan Normal University, College of Mathematics and Computer Science, 410081, Changsha, Hunan, People’s Republic of China;Hunan Normal University, College of Mathematics and Computer Science, 410081, Changsha, Hunan, People’s Republic of China
Venue:
Computing
Year:
2010

Citing 0
Cited 2

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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 O(Δt 2 + h l ). A numerical example demonstrates the theoretical results.