Two-Level Algorithm in the Solution of the Initial Value Problem for Partial Differential Equations

摘要

An implicit linear multistep method is applied to semi-discretized (nonlinear) time-dependent partial differential equations. Using Newton iteration the nonlinear implicit relations are replaced by a sequence of linear equations. These linear equations are solved by the iterative use of low-level algorithm. An iteration method based on incomplete LU-decomposition is chosen as the relaxation method (smoothing operator) in the two-level algorithm. Using discrete Fourier analysis the convergence and smoothing properties of the relaxation method are investigated for a model problem. The numerical experiments illustrate the choice of some suitable operators and parameters in the two-level algorithm.