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Second-order time discretization with finite-element method for partial integro-differential equations with a weakly singular kernel

Published online by Cambridge University Press:  17 February 2009

Chang Ho Kim  and
U Jin Choi
Chang Ho Kim
Affiliation:
Department of Applied Mathematics ofKon-Kuk University, Danwol 322, Chungju 380–701, Korea.
U Jin Choi
Affiliation:
Department of Mathematics of KAIST, Kusong-Dong 373–1, Yousong-Gu, Taejon 305–701, Korea.
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Abstract

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We propose the second-order time discretization scheme with the finite-element approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the finite element method and the time discretization is based on the Crank-Nicolson scheme with a graded mesh. We show the stability of the scheme and obtain the second-order convergence result for the fully discretized scheme.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 4 , April 1999 , pp. 513 - 524
Copyright
Copyright © Australian Mathematical Society 1999

References

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