Application of the Osher-Engquist Difference Scheme and the Full Multigrid Method to a Two Dimensional Nonlinear Elliptic Model Equation

摘要

A nonlinear boundary value problem in two dimensions is considered. For the discretization of this boundary value problem, the Osher-Engquist difference scheme is used and the discrete equations are solved by a full multigrid method (FMGM). In the FMGM, a coarse to fine sequence of grids with uniform meshes is applied. The result obtained on a coarser grid serves as initial approximation to the solution on the finer grid. On each grid the discrete equations are solved by Newton iteration. The Newton equations are approximately solved by the iterative use of a linear multilevel algorithm. Numerical results are given and comparisons with the method of time steps show that the multigrid approach is far more efficient than the method with explicit time steps.