COMPARISON OF CONVERGENCE OF ADOMIAN DECOMPOSITION METHOD AND FOURTH ORDER RUNGE-KUTTA METHOD
P. M. WANJAU *
School of Biological and Physical Sciences, Moi University, Box 3900 Eldoret, Kenya
F. K. GATHERI
School of Mathematics and Actuarial Science, Technical University of Kenya, Box 52428 -00200, Nairobi, Kenya
K. O. AWUOR
School of Pure and Applied Sciences, Kenyatta University, Box 43844-00100 Nairobi, Kenya
*Author to whom correspondence should be addressed.
Fluid dynamics is an important aspect of applied physics and engineering. Topics related to fluid dynamics always give rise to differential equations. These problems tend to be difficult to solve, often with no known exact solution. As such researchers are continually looking for ways to accurately and effectively solve them. One newly developed method that shows potential in this application is the Adomian Decomposition Method (ADM). The method has an advantage of reducing the computational work while still maintaining the accuracy of numerical solution. In this paper we investigate the consistency and convergence of this method. Results obtained are compared with those of fourth order Runge-Kutta method. Illustration is done by considering an initial value, third order ordinary differential equation. The results obtained from the example indicate that ADM has a better convergence than fourth order Runge- Kutta method.
Keywords: Adomian decomposition method