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.


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