IJPAM: Volume 93, No. 4 (2014)
FOR IMPLICIT RUNGE-KUTTA METHODS
Department of Mathematics and Statistics
Faculty of Science
University of Jaffna
Abstract. Several iteration schemes have been proposed to solve the non-linear equations arising in the implementation of implicit Runge-Kutta methods. As an alternative to the modified Newton scheme, some iteration schemes with reduced linear algebra costs have been proposed A scheme of this type proposed in  avoids expensive vector transformations and is computationally more efficient. The rate of convergence of this scheme is examined in  when it is applied to the scalar test differential equation and the convergence rate depends on the spectral radius of the iteration matrix , a function of , where is the step-length. In this scheme, we require the spectral radius of to be zero at and at in the -plane in order to improve the rate of convergence of the scheme. New schemes with parameters are obtained for three-stage and four-stage Gauss methods. Numerical experiments are carried out to confirm the results obtained here.
Received: January 3, 2014
AMS Subject Classification: 65L04, 65L05
Key Words and Phrases: implementation, Gauss methods, rate of convergence, stiff systems
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DOI: 10.12732/ijpam.v93i4.4 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 525 - 540
This work is licensed under the Creative Commons Attribution International License (CC BY).