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A fully adaptive MOL-treatment of parabolic 1-D problems with extrapolation techniques. (English) Zbl 0939.65108
The author presents a fully adaptive method for the numerical solution of coupled systems of highly nonlinear parabolic differential equations in one space dimension. The standard finite difference method is used as basic space discretization. A linear implicit Euler method is used for time discretization. The basic discretizations in space and time are combined with extrapolation. The method avoids the solution of systems of nonlinear equations and allows an easy change of computational grid after each time step. The algorithm is implemented in the user friendly software package PDEXIM. Two numerical examples are included.

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
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