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

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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.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Wulan Li & Xu Da

Authors
  1. Wulan Li
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  2. Xu Da
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Corresponding author

Correspondence to Xu Da.

Additional information

Communicated by N. Yan.

This work was supported in part by the National Natural Science Foundation of China, contract grant number 10971062.

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Li, W., Da, X. Finite central difference/finite element approximations for parabolic integro-differential equations. Computing 90, 89–111 (2010). https://doi.org/10.1007/s00607-010-0105-0

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  • DOI: https://doi.org/10.1007/s00607-010-0105-0

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