IJPAM: Volume 101, No. 4 (2015)

A NON-LINEAR SCHEME BASED ON PROJECTION
METHOD FOR TWO STAGE GAUSS METHOD

R. Vigneswaran
Department of Mathematics and Statistics
Faculty of Science
University of Jaffna
SRI LANKA


Abstract. A variety of linear iteration schemes with reduced linear algebra costs 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 iteration scheme. In this paper, a non-linear scheme based on projection method is proposed to accelerate the convergence rates of linear iteration schemes. In particular, for an $s$-stage Runge-Kutta method, an $s$-step non-linear scheme is proposed, which is computationally more efficient. For two stage Gauss method, some theoretical results are established in order to improve the rate of convergence of linear iteration schemes. Finally, some numerical experiments are carried out to confirm the results established in this paper.

Received: September 25, 2014

AMS Subject Classification: 65L04, 65L05

Key Words and Phrases: implementation, projection method, non-linear scheme, rate of convergence, stiff systems

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DOI: 10.12732/ijpam.v101i4.2 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: 2015
Volume: 101
Issue: 4
Pages: 463 - 476


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