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

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  • Mickens, Ronald E.

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.

Suggested Citation

  • Mickens, Ronald E., 2001. "A nonstandard finite difference scheme for a nonlinear PDE having diffusive shock wave solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(4), pages 549-555.
    • Handle: RePEc:eee:matcom:v:55:y:2001:i:4:p:549-555
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