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

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.