Homotopy analysis and Homotopy Pad$acute{e}$ methods for two-dimensional coupled Burgers\' equations

Homotopy Analysis Method for Solving Coupled Ramani Equations

A. JAFARIAN1, P. GHADERI2, ALIREZA K. GOLMANKHANEH3, D. BALEANU4,5,6 1Department of Mathematics, Uremia Branch, Islamic Azan University, Uremia, Iran E-mail: [email protected] 2Department of Mathematics, Uremia Branch, Islamic Azan University, Uremia, Iran E-mail: [email protected] 3Department of Physics, Uremia Branch, Islamic Azan University, P.O.BOX 969, Uremia, Iran E-mail: alir...

Homotopy Analysis Sumudu Transform Method for Nonlinear Equations

Homotopy Analysis Method for Solving Kdv Equations

A scheme is developed for the numerical study of the Korteweg-de Vries (KdV) and the Korteweg-de Vries Burgers (KdVB) equations with initial conditions by a homotopy approach. Numerical solutions obtained by homotopy analysis method are compared with exact solution. The comparison shows that the obtained solutions are in excellent agreement.

Higher-Order Numerical Solution of Two-Dimensional Coupled Burgers’ Equations

We proposed a higher-order accurate explicit finite-difference scheme for solving the two-dimensional heat equation. It has a fourth-order approximation in the space variables, and a secondorder approximation in the time variable. As an application, we developed the proposed numerical scheme for solving a numerical solution of the two-dimensional coupled Burgers’ equations. The main advantages ...

Homotopy Perturbation Method for Solving Systems of Nonlinear Coupled Equations

In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical and engineering problems linear and nonlinear. In this article, we shall use the homotopy perturbation method (HPM) to solve some systems of partial differential equations viz. the systems of coupled Burgers’ equations in oneand twodimensions and the system of Laplace’s equation. This a...

Homotopy Perturbation Method for the Coupled Fractional Lotka-volterra Equations

Fractional differential equations started to have important applications in various fields of science and engineering involving dynamics of complex phenomena. Finding new methods to solve the fractional differential equations is an open issue in the area of fractional calculus. In this paper the homotopy perturbation method is used to find an analytic approximate solution for the coupled Lotka-...