Using Multistage Laplace Adomian Decomposition Method to Solve Chaotic Financial System
Bonyah Ebenezer *
Department of Mathematics and Statistics, Kumasi Polytechnic, Kumasi, Ghana.
O. T. Kolebaje
Department of Physics, Adeyemi College of Education, Ondo, Nigeria.
Kwasi Awuah-Werekoh
Business School, Ghana Institute of Management and Public Administration, Accra, Ghana.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a new reliable algorithm, multistage Laplace Adomian decomposition method (MLADM) based on standard Laplace – Adomian method, is presented to solve a time- fractional financial model for both chaotic and non- chaotic. The new algorithm is just a simple modification of Laplace- Adomian method (LAM). This method is considered as an algorithm in a sequence of small intervals for obtaining accurate approximate solutions. The study depicts that the LADM provides reliable results for t ˂˂ 1. Numerical comparisons between the MLADM and the classical Runge- Kutta fourth order method (RK4) in the case of integer-order derivatives solutions indicates that the MLADM gives better output with high accuracy and is a promising technique for nonlinear systems of integer and fractional order.
Keywords: Laplace Adomian decomposition method, Runge- Kutta fourth order method, Laplace- Adomian method, Riemann Liouville integral, Chaos theory.