Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation

Abstract

In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.

An Analytical Technique to Solve the System of Nonlinear Fractional Partial Differential Equations

“…The homotopy analysis method have been described in [7] for solving KdV equations. The exact solution of KdV has been investigated in [8] using the variational iteration method. The analytical solution for a generalized coupled system of Zakharov-Kuznetsov and KdV equations have been obtained in [9] using the modified extended tanh method.…”

Explicit Expression for a First Integral for a Class of Two-dimensional Differential System

“…One of the classical tools in the classification of all trajectories of a dynamical system is to find first integrals. For more details about first integral see for instance [3,5,8,11,12,14] , see the references quoted in those articles. We recall that in the phase plane, a limit cycle of system (1) is an isolated periodic orbit in the set of all periodic orbits of system (1) System (1) is integrable on an open set Ω of R 2 if there exists a non constant C 1 function H : Ω → R, called a first integral of the system on Ω , which is constant on the trajectories of the system (1) contained in Ω, i.e.…”

Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula

“…A comparison was made between Adomian decomposition and tau methods in [4] for finding the solution of Volterra integro-differential equations. Magdy and Mohamed [20] practiced Laplace decomposition method and Pade approximation to get the numerical solution of nonlinear system of partial differential equations.…”