A Petrov--Galerkin method for integro-differential equations with a memory term

Kassem Mustapha

Abstract


We investigate the numerical solution of an integro-differential equation with a memory term. For the time discretization we apply the continuous Petrov--Galerkin method considered by Lin et al. [SIAM J. Numer. Anal., 38, 2000]. We combined the Petrov--Galerkin scheme with respect to time with continuous finite elements for the space discretization and obtained a fully discrete scheme. We show optimal error bounds of the numerical solutions for both schemes, and compare our theoretical error bounds with the results of numerical computations.

References
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  • T. Lin, Y. Lin, M. Rao and S. Zhang, Petrov-Galerkin methods for linear Volterra integro-differential equations, SIAM J. Numer. Anal., 38, 937--963 (2000). doi:10.1137/S0036142999336145
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DOI: http://dx.doi.org/10.21914/anziamj.v50i0.1382



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