M. Mohamed KHADER, Aml SHLOOF, Halima ALİ

On the numerical simulation and convergence study for system of non-linear fractional dynamical model of marriage

In this article, an implementation of an efficient numerical method for solving the system of coupled non-linear fractional (Caputo sense) dynamical model of marriage (FDMM) is introduced. The proposed system describes the dynamics of love affair between couples. The method is based on the spectral collocation method using Legendre polynomials. The proposed method reduces FDMM to a system of algebraic equations, which solved using Newton iteration method. Special attention is given to study the convergence analysis and deduce an error upper bound of the resulting approximate solution. Numerical simulation is given to show the validity and the accuracy of the proposed method.

Keywords:

Coupled non-linear fractional dynamical model of marriage, Caputo fractional derivatives, Legendre collocation method,

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