Results 61 to 70 of about 33,166 (180)

Homotopy Analysis Method for the Time-Fractional Boussinesq Equation

Universal Journal of Mathematics and Applications, 2020
In this paper, the exact and approximate analytical solutions to the time-fractional Boussinesq equation are constructed using the homotopy analysis method. Several examples about the fourth-order and sixth-order time-fractional Boussinesq equations show
He Yang
doaj   +1 more source

Application of homotopy analysis method for solving nonlinear Cauchy problem [PDF]

Surveys in Mathematics and its Applications, 2012
In this paper, by means of the homotopy analysis method (HAM), the solutions of some nonlinear Cauchy problem of parabolic-hyperbolic type are exactly obtained in the form of convergent Taylor series.
V.G. Gupta, Sumit Gupta
doaj  

Initialization Strategy for Nonlinear Systems [PDF]

, 2011
The Study Group was asked to provide some hints concerning a choice of initial values to be used for nonlinear algebraic systems. The group has considered the available options and outlined the pros and cons of various methods and provided some ...
Coskun, E.
core  

On Spectral Homotopy Analysis Method for Solving Linear Volterra and Fredholm Integrodifferential Equations

Abstract and Applied Analysis, 2012
A modification of homotopy analysis method (HAM) known as spectral homotopy analysis method (SHAM) is proposed to solve linear Volterra integrodifferential equations.
Z. Pashazadeh Atabakan, A. Kılıçman, A. Kazemi Nasab   +2 more
doaj   +1 more source

Numerical solution of time- and space-fractional coupled Burgers’ equations via homotopy algorithm

Alexandria Engineering Journal, 2016
In this paper, we constitute a homotopy algorithm basically extension of homotopy analysis method with Laplace transform, namely q-homotopy analysis transform method to solve time- and space-fractional coupled Burgers’ equations.
Jagdev Singh, Devendra Kumar, Ram Swroop
doaj   +1 more source

Analytical treatment of system of KdV equations by Homotopy Perturbation Method (HPM) and Homotopy Analysis Method (HAM) [PDF]

Computational Ecology and Software, 2014
In this article the Homotopy Perturbation Method (HPM) and Homotopy Analysis Method (HAM) are applied to obtain analytic approximate solution to three system of nonlinear wave equations, namely two component evolutionary system of a homogeneous KdV ...
Hafiz Abdul Wahab, Tahir Khan, Muhammad Shakil, et al.   +2 more
doaj  

Solving generalized quintic complex Ginzburg–Landau equation by homotopy analysis method

Ain Shams Engineering Journal, 2018
In this paper, the generalized quintic complex Ginzburg–Landau equation is considered to be solved, by means of the homotopy analysis method (HAM). Two examples are solved to illustrate the efficiency of the proposed method.
Soheila Naghshband, Mohammad Ali Fariborzi Araghi   +1 more
doaj   +1 more source

Spherical Hybrid Nanoparticles for Homann Stagnation-Point Flow in Porous Media via Homotopy Analysis Method. [PDF]

Nanomaterials (Basel), 2023
You X, Cui J.
europepmc   +1 more source

Homotopy analysis method for Cauchy Riemann equations

International Journal of Mathematical Analysis, 2014
In this paper, we obtain the series solution for the Cauchy Riemann equations with initial value problem by using homotopy analysis method (HAM), and computer graphics show that the HAM is efficient in solving Cauchy - Riemann equations.
Liu Xuan, Haidong Qu
openaire   +1 more source

The essence of the homotopy analysis method [PDF]

Applied Mathematics and Computation, 2010
The generalized Taylor expansion including a secret auxiliary parameter $h$ which can control and adjust the convergence region of the series is the foundation of the homotopy analysis method proposed by Liao. The secret of $h$ can't be understood in the frame of the homotopy analysis method. This is a serious shortcoming of Liao's method. We solve the
openaire   +2 more sources