Reduced Differential Transform Method for (2+1) Dimensional type of the Zakharov-Kuznetsov ZK(n,n) Equations

In this paper, reduced differential transform method (RDTM) is employed to approximate the solutions of (2+1) dimensional type of the Zakharov-Kuznetsov partial differential equations. We apply these method to two examples. Thus, we have obtained numerical solution partial differential equations of Zakharov-Kuznetsov. These examples are prepared to show the efficiency and simplicity of the method

An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method

In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value problems. The proposed approach is based on a Hermite function collocation (HFC) method. To illustrate the reliability of the method, some special cases of the equations are solved as test examples. The new method reduces the solution of a problem to the solution of a system of algebraic equations. Hermite functions have prefect properties that make them useful to achieve this goal. We compare the present work with some well-known results and show that the new method is efficient and applicable.Comment: 34 pages, 13 figures, Published in "Computer Physics Communications

Optimal Perturbation Iteration Method for Bratu-Type Problems

In this paper, we introduce the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. The proposed method is illustrated by studying Bratu-type equations. Our results show that only a few terms are required to obtain an approximate solution which is more accurate and efficient than many other methods in the literature.Comment: 11 pages, 3 Figure

Application of Homotopy Perturbation and Modified Adomian Decomposition Methods for Higher Order Boundary Value Problems

This work considers the numerical solution of higher order boundary value problems using Homotopy perturbation method (HPM) and modified Adomian decomposition method (MADM). HPM is applied without any transformation or calculation of Adomian polynomials. The differential equations are transformed into an infinite number of simple problems without necessarily using the perturbation techniques. Two numerical examples are solved to illustrate the method and the results are compared with the exact and MADM solutions. The accuracy and rapid convergence of HPM in handling the equations without calculating Adomian polynomials reveals its advantage over MAD