Stabilization of explicit methods for convection diffusion equations by discrete mollification

Authors:
Carlos D. Acosta;Carlos E. Mejía
Affiliations:
Universidad Nacional de Colombia, Department of Mathematics and Statistics, Manizales, Colombia;Universidad Nacional de Colombia, Department of Mathematics, Medellín, Colombia
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

The main goal of this paper is to show that discrete mollification is a simple and effective way to speed up explicit time-stepping schemes for partial differential equations. The second objective is to enhance the mollification method with a variety of alternatives for the treatment of boundary conditions. The numerical experiments indicate that stabilization by mollification is a technique that works well for a variety of explicit schemes applied to linear and nonlinear differential equations.