A fully adaptive MOL-treatment of parabolic 1-D problems with extrapolation techniques Original Research Article

A fully adaptive method is presented for the numerical solution of highly nonlinear, coupled systems of parabolic differential equations in one space dimension. Time discretization is by means of the linearly implicit Euler discretization. Space discretization is by finite differences on nonuniform grids. Both basic discretizations are combined with extrapolation. Based on local error estimates for both the time and the space discretization error, the accuracy of the numerical approximation is controlled and the discretization stepsizes are adapted automatically and simultaneously. The algorithm is implemented in a user friendly software package, PDEX1M.