Smoothed Runge-Kutta Methods in the Method of Lines

摘要

The effect of introducing smoothing matrices into Runge-Kutta methods for solvingsemidiscrete partial differential equations is investigated. Stability and accuracy are focussed upon. It is shown that the stiffness of the initial value problem can be removed by inserting simply structured smoothing matrices that are designed for use on vector computers so that the increase of the computational costs is rather modest. A number of explicitly given methods together with their smoothing error and stability boundaries are given. Numerical examples illustrate the theoretical results.