Vol. 12(3). Feb. 2021, No. 9, pp. 1-10.

NUMERICAL APPROACH OF NONLINEAR FRACTIONAL INITIAL VALUE PROBLEMS BY COMBINATION OF THE TWO METHODS : ADOMIAN DECOMPOSITION METHOD AND JACOBI SPECTRAL COLLOCATION
Vol. 12(3) ICMSFC Feb. 2021, No. 9, pp. 1-10
A. S. ALGHAMDI, J.F. ALZAIDY, A.K. HUSSAIN

Abstract

This paper expands a numerical method that is proposed in [1] to obtain approximate solutions of initial value problems for nonlinear fractional differential equations. This approach is based on the combination of the two methods: Adomian decomposition method and Jacobi spectral collocation method. The aim of this approach is to reduce the nonlinear differential equation to a system of algebraic equations that can be solved using a numerical method. Several examples with numerical solutions are provided to demonstrate the efficiency of this approach.


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