Exact and numerical solutions for non-linear Burger’s equation by VIM

Exact and numerical solutions for non-linear Burger's equation by VIM

In this article variational iterationmethod (VIM), established by He in (1999), is considered to solve nonlinear Bergur’s equation. This method is a powerful tool for solving a large number of problems. Using variational iteration method, it is possible to find the exact solution or a closed approximate solution of a problem. Comparing the results with those of Adomian’s decomposition and finit...

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

On the Analytical and Numerical Solutions of the One-Dimensional Non- linear Burgers' Equation

In this paper, we present two methods for finding solutions to the one-dimensional nonlinear Burgers’ equation. The first method is an analytical one, which is based on the tanh – function method. The second method is based on the Adomian decomposition method where two approaches are introduced. The first approach considers the use of the initial condition while the other considers the use of t...

Error analysis of approximate solutions of non-linear Burgers' equation

This paper deals with application of the maximum principle for differential equations to the finite difference method for determining upper and lower approximate solutions of the non-linear Burgers’ equation and their error range. In term of mathematical architecture, the paper is based on the maximum principle for parabolic differential equations to establish monotonic residual relations of th...

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow