Export Citations
Save this search
Please login to be able to save your searches and receive alerts for new content matching your search criteria.
- research-articleMarch 2024
Unsteady flow of hybrid-nanofluid in a non-homogeneous porous medium
International Journal of Computing Science and Mathematics (IJCSM), Volume 19, Issue 2Pages 146–156https://doi.org/10.1504/ijcsm.2024.137259This paper presents an unsteady flow of a Cu-Ag hybrid nanofluid flowing in a porous regime having variable permeability. The flow is pressure driven as well as time dependent. Two cases of variation in permeability are taken: exponential decay and ...
- research-articleJanuary 2021
An efficient particle swarm optimization with homotopy strategy for global numerical optimization
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology (JIFS), Volume 40, Issue 3Pages 4301–4315https://doi.org/10.3233/JIFS-200979Particle swarm optimization (PSO) as a successful optimization algorithm is widely used in many practical applications due to its advantages in fast convergence speed and convenient implementation. As a population optimization algorithm, the quality of ...
- research-articleJanuary 2021
Homotopy analysis method approximate solution for fuzzy pantograph equation
International Journal of Computing Science and Mathematics (IJCSM), Volume 14, Issue 3Pages 286–300https://doi.org/10.1504/ijcsm.2021.119904This paper investigates the powerful method namely the homotopy analysis method (HAM), to solve the fuzzy pantograph equation (FPE) in approximate analytic form. HAM yields a convergent infinite series solution to the solution of FPE without the need to ...
- research-articleJanuary 2020
Homotopy solution for MHD mixed convective unsteady flow of a Powell-Eyring fluid in a vertical porous space with oscillating wall temperature
International Journal of Computing Science and Mathematics (IJCSM), Volume 12, Issue 1Pages 21–35https://doi.org/10.1504/ijcsm.2020.108782In this paper, unsteady magnetohydrodynamic (MHD) flow of Powell-Eyring fluid in a vertical channel with diffusion thermo and thermal diffusion effects in the presence of heat source have been studied. The governing nonlinear, coupled partial differential ...
- ArticleSeptember 2015
Homotopy Analysis Method for Stochastic Differential Equations with Maxima
CASC 2015: Proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing - Volume 9301Pages 233–244https://doi.org/10.1007/978-3-319-24021-3_18The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian stochastic forces. It ...
- articleJuly 2013
Efficient computational algorithms for solving one class of fractional boundary value problems
Computational Mathematics and Mathematical Physics (CMMP), Volume 53, Issue 7Pages 920–932https://doi.org/10.1134/S0965542513070117In this paper, we introduce a modification of He's variational iteration, homotopy analysis and optimal homotopy analysis methods for solving fractional boundary value problems. It is illustrated that the proposed methods are powerful fast numerical ...
- articleMay 2011
Approximate analytical solutions to thermo-poroelastic equations by means of the iterated homotopy analysis method
International Journal of Computer Mathematics (IJOCM), Volume 88, Issue 8Pages 1763–1775https://doi.org/10.1080/00207160.2010.526706A new approach of the homotopy analysis method (HAM), named iterated homotopy analysis method (I-HAM) is used to find approximate analytical solutions to thermo-poroelastic equations. The homotopy analysis method contains the auxiliary parameter ℏ, ...
- articleFebruary 2011
Homotopy analysis method for solving fractional hyperbolic partial differential equations
International Journal of Computer Mathematics (IJOCM), Volume 88, Issue 3Pages 578–588https://doi.org/10.1080/00207161003631901In the present paper, the solutions of the hyperbolic partial differential equation with fractional time derivative of order α (1<α≤2) are obtained with the help of approximate analytical method of nonlinear problems called the homotopy analysis method. ...
- articleJanuary 2011
Application of homotopy perturbation method and homotopy analysis method to fractional vibration equation
In this paper, the approximate analytical solutions of the mathematical model of vibration equation with fractional-order time derivative ß (1
- articleJanuary 2011
The homotopy analysis method and the Lienard equation
International Journal of Computer Mathematics (IJOCM), Volume 88, Issue 1Pages 121–134https://doi.org/10.1080/00207160903248659In this article, Lienard equations are considered. The limit cycles of these systems are studied by applying the homotopy analysis method (HAM). The amplitude and frequency obtained with this methodology are in good agreement with those calculated by ...
- articleAugust 2010
Solitary-wave solutions of the Degasperis-Procesi equation by means of the homotopy analysis method
International Journal of Computer Mathematics (IJOCM), Volume 87, Issue 10Pages 2303–2313https://doi.org/10.1080/00207160802626492The homotopy analysis method (HAM) is applied to the Degasperis-Procesi equation in order to find analytic approximations to the known exact solitary-wave solutions for the solitary peakon wave and the family of solitary smooth-hump waves. It is ...
- ArticleJuly 2010
Flow of a micropolar fluid in channel with heat and mass transfer
The problem of micropolar fluid flow in a channel subject to a chemical reaction is presented. The effect of small and large Peclet numbers on the temperature and concentration profiles is determined while the effects of various parameters such as the ...
- articleJune 2009
Homotopy analysis method for systems of fractional integro-differential equations
In this article, based on the homotopy analysis method (HAM), a new analytic technique is proposed to solve systems of fractional integro-differential equations. Comparing with the exact solution, the HAM provides us with a simple way to adjust and ...
- research-articleMay 2009
On the interaction of deep water waves and exponential shear currents
Zeitschrift für Angewandte Mathematik und Physik (ZAMP) (ZAMP), Volume 60, Issue 3Pages 450–478https://doi.org/10.1007/s00033-008-7050-1Abstract.A train of periodic deep-water waves propagating on a steady shear current with a vertical distribution of vorticity is investigated by an analytic method, namely the homotopy analysis method (HAM). The magnitude of the vorticity varies ...
- ArticleDecember 2008
Series solution of nonlinear dynamic system containing fractional derivative
Series solution of nonlinear dynamic system containing fractional derivative is obtained by the homotopy analysis method (HAM). The solution via HAM has auxiliary parameter h which can control the convergent of the series to obey the exact or numerical ...
- research-articleJanuary 2008
Homotopy analysis method for generalized Benjamin–Bona–lMahony equation
Zeitschrift für Angewandte Mathematik und Physik (ZAMP) (ZAMP), Volume 59, Issue 1Pages 51–62https://doi.org/10.1007/s00033-007-6115-xAbstract.An analytic technique, the homotopy analysis method (HAM), is applied to solve the generalized Benjamin–Bona–Mahony (BBM) equation. An explicit series solution is given, different from traditional analytic techniques, our approach is independent ...
- research-articleNovember 2005
On non-linear flows with slip boundary condition
Zeitschrift für Angewandte Mathematik und Physik (ZAMP) (ZAMP), Volume 56, Issue 6Pages 1012–1029https://doi.org/10.1007/s00033-005-4006-6Abstract.The assumption that a fluid adheres to a solid boundary (‘no-slip’ boundary condition) is one of the central tenets of the Navier-Stokes theory. However, there are situations wherein this assumption does not hold. In this communication we examine ...