Implementation to the Different Differential Equations of Homotopy Analysis , Differential Transformed and Adomian Decomposition Method
نویسنده
چکیده
In this study, the concept of Homotopy analysis method (HAM) is briefly introduced. Furthermore some non-linear problems are handled and the solutions of these problems are given using by HAM, DTM, ADM methods and the convergence of the solution is shown to the exact solution. Additionally, the three methods are compared and it is observed that the HAM is more-less efficient and effective than the ADM and DTM in according to the exact solution. In the end, some of the numerical solutions of two examples are presented and the results are shown in graphs and figures.
منابع مشابه
Comparison of acceleration techniques of analytical methods for solving differential equations of integer and fractional order
The work addressed in this paper is a comparative study between convergence of the acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on Homotopy analysis method and Adomian decomposition method for solving differential equations of integer and fractional orders.
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 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 کاملA Comparison Between Fourier Transform Adomian Decomposition Method and Homotopy Perturbation ethod for Linear and Non-Linear Newell-Whitehead-Segel Equations
In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is ...
متن کاملStudy on efficiency of the Adomian decomposition method for stochastic differential equations
Many time-varying phenomena of various fields in science and engineering can be modeled as a stochastic differential equations, so investigation of conditions for existence of solution and obtain the analytical and numerical solutions of them are important. In this paper, the Adomian decomposition method for solution of the stochastic differential equations are improved. Uniqueness and converg...
متن کاملSOLUTION OF FUZZY DIFFERENTIAL EQUATIONS UNDER GENERALIZED DIFFERENTIABILITY BY ADOMIAN DECOMPOSITION METHOD
Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. We interpret a fuzzy differential equation by using the strongly generalized differentiability. Also one concrete application for ordinary fuzzy differential equation with fuzzy input data...
متن کامل