An invariant moving mesh scheme for the nonlinear diffusion equation
The main purpose of the paper is to present some theoretical and numerical aspects of the Cauchy problem for the nonlinear diffusion equation \(u_t= (u^mu_x)_x\), \(m\in\mathbb{R}\), \(m>-2\), which is posed on an infinite domain. When solving such problems one can use the information given by the invariance of this problem to a Lie group of stretchings. The problem is semi-discretized using the method of lines and the discrete solutions are desired to have the same asymptotic behaviour as solutions of the continuous problem. Hence the main role plays the fact that the derived scheme has the same conserved quantities and the same invariants as the continuous problem. (Shortened review; the full text is available at Zbl).
scientific article; zbMATH DE number 1115977
scientific article