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A Third Order Method for Convection-Diffusion Equations with a Delay Term

In: Numerical Mathematics and Advanced Applications

Author

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  • J. Frochte

    (Fachhochschule Südwestfalen, Elektrische Energietechnik Soest)

Abstract

The numerical solution of a parabolic convection diffusion equation with delay term is considered. This includes both variants, the initial value problem and the prehistory problem. Equations with a delay or memory term, often called integrodifferential problems, appear in different contexts of heat conduction in materials with memory, viscoelasticity and population models. This work concentrates on the linear convection diffusion case of the prehistory and the initial value problem. One problem concerning delay or memory problems is the data storage. To deal with this problem an adaptivity method of third order in time is developed to save storage data at smooth parts of the solution. Numerical results for higher Péclet numbers are presented.

Suggested Citation

  • J. Frochte, 2008. "A Third Order Method for Convection-Diffusion Equations with a Delay Term," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 281-288, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_33
    DOI: 10.1007/978-3-540-69777-0_33
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