A nonstandard finite difference scheme for a nonlinear PDE having diffusive shock wave solutions

Ronald E. Mickens

Mathematics and Computers in Simulation (MATCOM), 2001, vol. 55, issue 4, 549-555

Abstract: Nonlinear diffusion processes can give rise to shock wave type solutions. These solutions are usually derived from the application of similarity methods since general solutions to the relevant partial differential equations are not known. We consider the Boltzmann problem and construct an exact finite difference scheme for the ordinary differential equation obtained from the use of similarity and investigate its properties.

Keywords: Nonlinear diffusion; Finite difference schemes; Nonlinear waves; Shocks (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:55:y:2001:i:4:p:549-555

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