A Petrov–Galerkin method for integro-differential equations with a memory term
نویسنده
چکیده
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. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1382 gives this article, c © Austral. Mathematical Soc. 2008. Published December 22, 2008. issn 1446-8735. (Print two pages per sheet of paper.)
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