A new variable step size algorithm for solving initial value problems. | [Journal of Basic and Applied Sciences • 2006]

Author(s):

1. Khurram Kamran: Department of Mathematics, University of Karachi, Karachi, Pakistan

2. M. Shahid Qureshi: Institute of Space & Planetary Astrophysics, University of Karachi, Karachi, Pakistan

3. Nasir Touheed: Department of Computer Science, University of Karachi, Karachi, Pakistan

Abstract:

Polynomials constructed by usual interpolation methods are less accurate as compared to the tools due to Chebyshev. Hence the use of Chebychev’s nodes to produce the solution of Initial Value Problems promises more accurate results. In this work a new algorithm is developed using nodes generated by Chebychev’s method that are used as point where solutions are produced for a number of Linear and Non-Linear Initial Value Problems using classical Runge-Kutta method. The improvement in accuracy is found even when the number of nodes is small, that makes this algorithm better than other variable step-size methods.

Page(s): 37-44

DOI: DOI not available

Published: Journal: Journal of Basic and Applied Sciences, Volume: 2, Issue: 1, Year: 2006

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