Results 1 to 10 of about 33,166 (180)

An approximate analytical solution of the Allen-Cahn equation using homotopy perturbation method and homotopy analysis method [PDF]

Heliyon, 2019
In this paper, an approximate analytical solution of the bistable Allen–Cahn equation is given. The Allen–Cahn equation is a mathematical model to study the phase separation process in binary alloys and emerged as a convection-diffusion equation in fluid
Safdar Hussain, Abdullah Shah, Sana Ayub, Asad Ullah   +3 more
doaj   +4 more sources

Convergence of the homotopy analysis method [PDF]

, 2010
The homotopy analysis method is studied in the present paper. The question of convergence of the homotopy analysis method is resolved. It is proven that under a special constraint the homotopy analysis method does converge to the exact solution of the sought solution of nonlinear ordinary or partial differential equations.
Turkyilmazoglu, Mustafa
openaire   +3 more sources

Homotopy Analysis Method for Time-Fractional Schrödinger Equations

Walailak Journal of Science and Technology, 2012
The Homotopy Analysis Method (HAM) is applied to tackle time-fractional Schrödinger equations. The proposed technique is fully compatible with the complexity of these problems and obtained results are highly encouraging.
Nauman ASGHAR, Kamran ALI, Ahmet YILDIRIM, Syed Tauseef MOHYUD-DIN   +3 more
doaj   +3 more sources

Homotopy analysis method for solving KdV equations [PDF]

Surveys in Mathematics and its Applications, 2010
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.
Hossein Jafari, M. A. Firoozjaee
doaj   +2 more sources

Revisiting Fisher-KPP model to interpret the spatial spreading of invasive cell population in biology

Heliyon, 2022
In this paper, the homotopy analysis method, a powerful analytical technique, is applied to obtain analytical solutions to the Fisher-KPP equation in studying the spatial spreading of invasive species in ecology and to extract the nature of the spatial ...
Gour Chandra Paul, Tauhida, Dipankar Kumar   +2 more
doaj   +1 more source

Variational homotopy perturbation method for solving systems of homogeneous linear and nonlinear partial differential equations

Desimal, 2021
The variational homotopy perturbation method is developed by combining variational iteration method and homotopy perturbation method. Variational iteration method has an efficient process in solving a wide variety of equations and systems of equations ...
Atika Faradilla, Aang Nuryaman, Asmiati Asmiati, Dewi Rakhmatia Nur   +3 more
doaj   +1 more source

A robust computational approach for Zakharov-Kuznetsov equations of ion-acoustic waves in a magnetized plasma via the Shehu transform

Journal of Ocean Engineering and Science, 2023
The application of the q-homotopy analysis Shehu transform method (q-HAShTM) to discover the estimated solution of fractional Zakharov-Kuznetsov equations is investigated in this study.
Parthkumar P. Sartanpara, Ramakanta Meher   +1 more
doaj   +1 more source

Time-fractional partial differential equations: a novel technique for analytical and numerical solutions

Arab Journal of Basic and Applied Sciences, 2022
We use the q-homotopy analysis Shehu transform method in this article to obtain analytical and numerical solutions to time fractional partial differential equations.
Lokesh Kumar Yadav, Garima Agarwal, D. L. Suthar, S. D. Purohit   +3 more
doaj   +1 more source

Homotopy Analysis Aboodh Transform Method for Nonlinear System of Partial Differential Equations

Universal Journal of Mathematics and Applications, 2018
In this paper, a combined form of homotopy analysis method with Aboodh transform method is proposed to solve nonlinear system of partial differential equations. This method is called the homotopy analysis Aboodh transform method (HAATM).
Mountassir Hamdi Cherif, Djelloul Ziane
doaj   +1 more source

Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method [PDF]

, 2009
The homotopy analysis method is applied to the short-pulse equation in order to find an analytic approximation to the known exact solitary upright-loop solution. It is demonstrated that the approximate solution agrees well with the exact solution.
Abbasbandy, Abbasbandy, Abbasbandy, Abbasbandy, Abbasbandy, Abbasbandy, Abbasbandy, Abbasbandy, Hayat, Hayat, Hayat, Hayat, Hayat, Liao, Liao, Liao, Liao, Liao, Liao, Parkes, Sajid, Sajid, Sajid, Sakovich, Sakovich, Schäfer, Tan, Tan, Wadati, Wang, Wu   +30 more
core   +1 more source