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Cole-Hopf transformation as numerical tool for the Burgers equation. (English) Zbl 1187.65116

Summary: A numerical method solving the Burgers equation via the diffusion equation is proposed. The time variation of the numerical solution is given by a rational function. The coefficient of the polynomials in the denominator and numerator are determined by simple algebra. In the case of vanishingly small viscosity, the numerical method becomes shock-capturing only by increasing the viscosity to the order of mesh spacing locally around shocks. This procedure can be done automatically.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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