A Comparison Between Analytical and Numerical Solutions for Time-Fractional Coupled Dispersive Long-Wave Equations

Year 2021, Volume: 2 Issue: 1, 8 - 29, 29.01.2021

Medjahed Djilali , Hakem Alı , Benali Abdelkader

Abstract

In this article, a technique namely Tanh method is applied to obtain some traveling wave
solutions for coupled Dispersive Long-Wave equations, and by using LADM we obtain an approximate
solution to TFDLW (time-fractional DLW equations). A comparison between the traveling wave solution
and the approximate one of the DLW system indicates that Laplace Adomian Decomposition Method
(LADM) is highly accurate and can be considered a very useful and valuable method. The availability of
computer systems like Mathematica 11 software facilitates the tedious algebraic calculations and plots
of surfaces of solutions. The methods which we will propose in this paper are also standard, direct and
computerizable methods, which allows us to do complicated and tedious algebraic calculation.

Keywords

Adomian polynomials, Caputo's fractional derivative, Dispersive Long-Wave

Supporting Institution

Laboratory ACEDP, Djillali Liabes University, 22000 SIDI-BEL-ABBES, Algeria

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