Table of Contents
Journal of Computational Engineering
Volume 2013 (2013), Article ID 720812, 5 pages
http://dx.doi.org/10.1155/2013/720812
Research Article

An Implicit Method for Numerical Solution of Singular and Stiff Initial Value Problems

Department of Mathematics, Rajshahi University of Engineering and Technology, Rajshahi 6204, Bangladesh

Received 29 April 2013; Revised 27 August 2013; Accepted 30 August 2013

Academic Editor: Fu-Yun Zhao

Copyright © 2013 M. Kamrul Hasan et al. 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

An implicit method has been presented for solving singular initial value problems. The method is simple and gives more accurate solution than the implicit Euler method as well as the second order implicit Runge-Kutta (RK2) (i.e., implicit midpoint rule) method for some particular singular problems. Diagonally implicit Runge-Kutta (DIRK) method is suitable for solving stiff problems. But, the derivation as well as utilization of this method is laborious. Sometimes it gives almost similar solution to the two-stage third order diagonally implicit Runge-Kutta (DIRK3) method and the five-stage fifth order diagonally implicit Runge-Kutta (DIRK5) method. The advantage of the present method is that it is used with less computational effort.