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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 39246, 15 pages
http://dx.doi.org/10.1155/MPE/2006/39246

Analysis of linear and nonlinear stiff problems using the RK-Butcher algorithm

Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tanjore Road, Tiruchirappalli 620 015, Tamil Nadu, India

Received 25 July 2005; Accepted 10 November 2005

Copyright © 2006 S. Sekar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

I present a numerical solution of linear and nonlinear stiff problems using the RK-Butcher algorithm. The obtained discrete solutions using the RK-Butcher algorithm are found to be very accurate and are compared with the exact solutions of the linear and nonlinear stiff problems and also with the Runge-Kutta method based on arithmetic mean (RKAM). A topic of stability for the RK-Butcher algorithm is discussed in detail. Error graphs for discrete and exact solutions are presented in a graphical form to show the efficiency of the RK-Butcher algorithm. The results obtained show that RK-Butcher algorithm is more useful for solving linear and nonlinear stiff problems and the solution can be obtained for any length of time.