Accelerating the Rate of Convergence of a More General Linear Iteration Scheme by using the Projection Method for Implicit Runge-Kutta Methods

Abstract

Various iteration schemes arc proposed by vanous authors to solve non-linear equations arising in the implementation of im lJlicit Runge-Kutta methods. In this Ilaller, a class of general non-linear scheme based on 11rojcrtion method is proposed to accelerate the rate of convergencc of already prollosed more general linear iteration scheme. Theoretical results arc established in order to improve the rate of convergence of linear iteration schemes for two, three and four stage Gauss method. To confirm the results established in this Ila ller, some numerical eXlleriments arc carried out.