Using Multistage Laplace Adomian Decomposition Method to Solve Chaotic Financial System

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.