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

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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