A Review of Some Recent Results for the Approximate Analytical Solutions of Nonlinear Differential Equations
نویسندگان
چکیده
This paper features a survey of some recent developments in techniques for obtaining approximate analytical solutions of some nonlinear differential equations arising in various fields of science and engineering. Adomian’s decomposition method is applied to some nonlinear problems, and some mathematical tools such as He’s homotopy perturbation method and variational iteration method are introduced to overcome the shortcomings of Adomian’s method. The results of some comparisons of these three methods appearing in the research literature are given.
منابع مشابه
An Approximate Method for System of Nonlinear Volterra Integro-Differential Equations with Variable Coefficients
In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...
متن کاملAnalytical-Approximate Solution for Nonlinear Volterra Integro-Differential Equations
In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...
متن کاملTHE ELZAKI HOMOTOPY PERTURBATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS
In this paper, Elzaki Homotopy Perturbation Method is employed for solving linear and nonlinear differential equations with a variable coffecient. This method is a combination of Elzaki transform and Homotopy Perturbation Method. The aim of using Elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as Homotopy Perturbat...
متن کاملDirichlet series and approximate analytical solutions of MHD flow over a linearly stretching sheet
The paper presents the semi-numerical solution for the magnetohydrodynamic (MHD) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. The governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (NODE) by using a classical similarity transformation along with appropriate boundary cond...
متن کاملAnalytical solution of MHD flow and heat transfer over a permeable nonlinearly stretching sheet in a porous medium filled by a nanofluid
In this paper, the differential transform method and Padé approximation (DTM-Padé) is applied to obtain the approximate analytical solutions of the MHD flow and heat transfer of a nanofluid over a nonlinearly stretching permeable sheet in porous. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations...
متن کاملUsage of the Variational Iteration Technique for Solving Fredholm Integro-Differential Equations
Integral and integro-differential equations are one of the most useful mathematical tools in both pure and applied mathematics. In this article, we present a variational iteration method for solving Fredholm integro-differential equations. This study provides an analytical approximation to determine the behavior of the solution. To show the efficiency of the present method for our proble...
متن کامل