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Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
(Si10-123) Comparison Between The Homotopy Perturbation Method And Variational Iteration Method For Fuzzy Differential Equations, P. Chandru, B. Radhakrishnan
(Si10-123) Comparison Between The Homotopy Perturbation Method And Variational Iteration Method For Fuzzy Differential Equations, P. Chandru, B. Radhakrishnan
Applications and Applied Mathematics: An International Journal (AAM)
In this article, the authors discusses the numerical simulations of higher-order differential equations under a fuzzy environment by using Homotopy Perturbation Method and Variational Iteration Method. The fuzzy parameter and variables are represented by triangular fuzzy convex normalized sets. Comparison of the results are obtained by the homotopy perturbation method with those obtained by the variational iteration method. Examples are provided to demonstrate the theory.
Heat And Mass Transfer Effects Of Peristaltic Transport Of A Nano Fluid In Peripheral Layer, K. M. Prasad, N. Subadra, M, A. S. Srinivas
Heat And Mass Transfer Effects Of Peristaltic Transport Of A Nano Fluid In Peripheral Layer, K. M. Prasad, N. Subadra, M, A. S. Srinivas
Applications and Applied Mathematics: An International Journal (AAM)
This paper deals with a theoretical investigation of heat and mass transfer effects of peristaltic transport of a nanofluid in peripheral layer. By using appropriate methods, the velocity in the core region as well as in the peripheral region, pressure drop, time averaged flux, frictional force, temperature profile, nanoparticle phenomenon, heat transfer coefficient and mass transfer coefficient of the fluid are investigated, using lubrication theory. Effects of different physical parameters like viscosity ratio, mean radius of the central layer, Brownian motion parameter, thermophoresis parameter, local temperature Grashof number as well as local nanoparticle Grashof number on pressure rise characteristics, frictional …
A New Approach To The Numerical Solution Of Fractional Order Optimal Control Problems, T. Akbarian, M. Keyanpour
A New Approach To The Numerical Solution Of Fractional Order Optimal Control Problems, T. Akbarian, M. Keyanpour
Applications and Applied Mathematics: An International Journal (AAM)
In this article, a new numerical method is proposed for solving a class of fractional order optimal control problems. The fractional derivative is considered in the Caputo sense. This approach is based on a combination of the perturbation homotopy and parameterization methods. The control function u(t) is approximated by polynomial functions with unknown coefficients. This method converts the fractional order optimal control problem to an optimization problem. Numerical results are included to demonstrate the validity and applicability of the method.
Approximating Solutions For Ginzburg – Landau Equation By Hpm And Adm, J. Biazar, M. Partovi, Z. Ayati
Approximating Solutions For Ginzburg – Landau Equation By Hpm And Adm, J. Biazar, M. Partovi, Z. Ayati
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, an analytical approximation to the solution of Ginzburg-Landauis discussed. A Homotopy perturbation method introduced by He is employed to derive the analytic approximation solution and results compared with those of the Adomian decomposition method. Two examples are presented to show the capability of the methods. The results reveal that the methods are almost equally effective and promising.
Approximate Approach To The Das Model Of Fractional Logistic Population Growth, S. Das, P. K. Gupta, K. Vishal
Approximate Approach To The Das Model Of Fractional Logistic Population Growth, S. Das, P. K. Gupta, K. Vishal
Applications and Applied Mathematics: An International Journal (AAM)
In this article, the analytical method, Homotopy perturbation method (HPM) has been successfully implemented for solving nonlinear logistic model of fractional order. The fractional derivatives are described in the Caputo sense. Using initial value, the explicit solutions of population size for different particular cases have been derived. Numerical results show that the method is extremely efficient to solve this complicated biological model.
Numerical Comparison Of Methods For Hirota-Satsuma Model, Syed T. Mohyud-Din, Ahmet Yildirim, Syed M. Mahdi Hosseini
Numerical Comparison Of Methods For Hirota-Satsuma Model, Syed T. Mohyud-Din, Ahmet Yildirim, Syed M. Mahdi Hosseini
Applications and Applied Mathematics: An International Journal (AAM)
This paper outlines the implementation of the modified decomposition method (MDM) to solve a very important physical model namely Hirota-Satsuma model which occurs quite often in applied sciences. Numerical results and comparisons with homotopy perturbation (HPM) and Adomian’s decomposition (ADM) methods explicitly reveal the complete reliability of the proposed MDM. It is observed that the suggested algorithm (MDM) is more user-friendly and is easier to implement compared to HPM and ADM.
On The Solution Of The Vibration Equation By Means Of The Homotopy Perturbation Method, Ahmet Yıldırım, Canan Ünlü, Syed T. Mohyud-Din
On The Solution Of The Vibration Equation By Means Of The Homotopy Perturbation Method, Ahmet Yıldırım, Canan Ünlü, Syed T. Mohyud-Din
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present a reliable algorithm, the homotopy perturbation method, to solve the well-known vibration equation for very large membrane which is given initial conditions. By using initial value, the explicit solutions of the equation for different cases have been derived, which accelerate the rapid convergence of the series solution. Numerical results show that the homotopy perturbation method is easy to implement and accurate when applied to differential equations. Numerical results for different particular cases of the problem are presented graphically.
Homotopy Perturbation Method And The Stagnation Point Flow, P. Donald Ariel
Homotopy Perturbation Method And The Stagnation Point Flow, P. Donald Ariel
Applications and Applied Mathematics: An International Journal (AAM)
The laminar steady flow of an incompressible, viscous fluid near a stagnation point has been computed using the homotopy perturbation method (HPM). Both the cases, (i) two-dimensional flow and (ii) axisymmetric flow, have been considered. A sequence of successive approximations has been obtained in the solution, and the convergence of the sequence is achieved by using the Padé approximants. It is found that there is a complete agreement between the results obtained by the HPM and the exact numerical solution.
Latest Developments In Nonlinear Sciences, Syed T. Mohyud-Din, Ahmet Yildirim
Latest Developments In Nonlinear Sciences, Syed T. Mohyud-Din, Ahmet Yildirim
Applications and Applied Mathematics: An International Journal (AAM)
This paper outlines a detailed study of some latest trends and developments in nonlinear sciences. The major focus of our study will be variational iteration (VIM) and its modifications, homotopy perturbation (HPM), parameter expansion and exp-function methods. The above mentioned schemes are highly accurate, extraordinary efficient, capable to cope with the versatility of the physical problems and are being used to solve a wide class of nonlinear problems. Several examples are given which reveal the justification of our claim.
Application Of Homotopy Analysis Method To Fourth-Order Parabolic Partial Differential Equations, M. Matinfar, M. Saeidy
Application Of Homotopy Analysis Method To Fourth-Order Parabolic Partial Differential Equations, M. Matinfar, M. Saeidy
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, by means of the homotopy analysis method (HAM), the solutions of some fourthorder parabolic partial differential equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter h that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.
An Efficient Technique For Solving Special Integral Equations, Jafar Biazar, Mostafa Eslami
An Efficient Technique For Solving Special Integral Equations, Jafar Biazar, Mostafa Eslami
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply a new technique for solving two-dimensional integral equations of mixed type. Comparisons are made between the homotopy perturbation method and the new technique. The results reveal that the new technique is effective and convenient.
Homotopy Perturbation Method And Padé Approximants For Solving Flierl-Petviashivili Equation, Syed T. Mohynd-Din, Muhammad A. Noor
Homotopy Perturbation Method And Padé Approximants For Solving Flierl-Petviashivili Equation, Syed T. Mohynd-Din, Muhammad A. Noor
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present a reliable combination of homotopy perturbation method and Padé approximants to investigate the Flierl-Petviashivili (FP) equation. The approach introduces a new transformation necessary for the conversion of the Flierl-Petviashivili equation to a first order initial value problem and a reliable framework designed to overcome the difficulty of the singular point at x = 0. The proposed homotopy perturbation method is applied to the reformulated first order initial value problem which leads the solution in terms of transformed variable. The desired series solution is obtained by making use of the inverse transformation. The suggested algorithm may …