High order explicit methods for parabolic equations
The author discusses how by use of Chebyshev alternation theory high-order explicit Runge-Kutta methods with a real stability interval as large as possible can be constructed. In particular, he presents methods of order three and four. He concludes with a report on their application to the large systems of ordinary differential equations (in time) obtained by spatial discretization of parabolic equations (e.g. the Burgers equation).
nonlinear parabolic differential equations
scientific article; zbMATH DE number 1206839