A singular perturbation of the heat equation with memory

Authors:
J. R. Branco;J. A. Ferreira
Affiliations:
Departamento de Física Matemática, Insituto Superior de Engenharia de Coimbra, Rua Pedro Nunes-Quinta da Nora, 3030-199 Coimbra, Portugal;Departamento de Matemática, Faculdade de Ciências e Tecnologia, Apartado 3008, 3000 Coimbra, Portugal
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In this paper we consider a hyperbolic equation, with a memory term in time, which can be seen as a singular perturbation of the heat equation with memory. The qualitative properties of the solutions of the initial boundary value problems associated with both equations are studied. We propose numerical methods for the hyperbolic and parabolic models and their stability properties are analyzed. Finally, we include numerical experiments illustrating the performance of those methods.