IJPAM: Volume 93, No. 4 (2014)
FOR IMPLICIT RUNGE-KUTTA METHODS



Faculty of Science
University of Jaffna
SRI LANKA
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 [9] avoids expensive vector transformations and is
computationally more efficient. The rate of convergence of this
scheme is examined in [9] 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
Year: 2014
Volume: 93
Issue: 4
Pages: 525 - 540
