On Efficient Time-Stepping Methods for Nonlinear Second Order Hyperbolic Partial Differential Equations

摘要

Techniques useful for efficiently time-stepping Galerkin methods for various types of time-dependent partial differential equations are presented and analyzed. Second-order quasilinear hyperbolic problems with smooth solutions are studied as a simple model problem for illustrating the widely applicable techniques. The procedure involves the use of a preconditioned iterative method for approximately solving the different linear systems of equations arising at each time-step in a discrete-time Galerkin method. Optimal order L2 spatial errors and almost optimal order work estimates are obtained for the second-order hyperbolic equation. (Author)