An approximate analytical solution of the Allen-Cahn equation using homotopy perturbation method and homotopy analysis method
نویسندگان
چکیده
منابع مشابه
The comparison of optimal homotopy asymptotic method and homotopy perturbation method to solve Fisher equation
In recent years, numerous approaches have been applied for finding the solutions of functional equations. One of them is the optimal homotopy asymptotic method. In current paper, this method has been applied for obtaining the approximate solution of Fisher equation. The reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...
متن کاملApproximate Analytical Solution of 3D Fractional Microscale Heat Equation Using Modified Homotopy Perturbation Method
In the present article, we use modified homotopy perturbation method (HPM) to find approximate analytical solution of three-dimensional time fractional microscale heat transport equation. This transport equation is at first converted into the equation of two functions. First one have both, the first order fractional time derivative and second order space derivatives, while second one has only s...
متن کاملApproximate Analytical Solution of Diffusion Equation with Fractional Time Derivative Using Optimal Homotopy Analysis Method
In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution...
متن کاملApproximate Analytical Solutions of the Regularized Long Wave Equation Using the Optimal Homotopy Perturbation Method
The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the h...
متن کاملA New Approximate Analytical Solution of Kuramoto – Sivashinsky Equation Using Homotopy Analysis Method
In this paper, Homotopy Analysis Method (HAM) is applied to obtain approximate analytical solution of modified Kuramoto–Sivashinsky (KS) equation. HAM provides a simple way to adjust and control the convergence region of the series solution by introducing several parameters, namely, the auxiliary parameter, h, the auxiliary function, H(x, t), the initial guess, u0(x, t) and the auxiliary linear...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Heliyon
سال: 2019
ISSN: 2405-8440
DOI: 10.1016/j.heliyon.2019.e03060