An Iteration Scheme for Implicit Runge—Kutta Methods

Abstract

In the implementation of implicit Runge-Kutta methods the computational effort is typically dominated by the cost of solving large sets of non-linear equations. As an alternative to the usual Newton method, an iteration scheme is considered that sacrifices superlinear convergence for reduced linear algebra costs. By modifying this new scheme, using the successive over-relaxation technique, an improvement is achieved in the rate of convergence.