Application of Homotopy Perturbation and Variational Iteration Methods for Fredholm Integrodifferential Equation of Fractional Order

Elbeleze, Asma Ali; Kılıçman, Adem; Taib, Bachok M.

doi:10.1155/2012/763139

Cited by 14 publications

(12 citation statements)

References 43 publications

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“…In the last years, many of the new methods were used for solving linear and nonlinear functional equations arising from the mathematical} modeling of problems in mathematics, physics, engineering, and other different science branches which have important applications in life such as Adomian decomposition method (ADM) [1,2], variational iteration method (VIM) [3][4][5][6][7], homotopy perturbation method (HPM) [8][9][10][11][12][13], homotopy analysis method (HAM) [8,14], new iterative method (NIM) [15][16][17][18][19][20][21], differential transform method (DTM) [22], Laplace transform method (LTM) [1,22], integral iterative method (IIM) [23,24], and other methods [25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

New Iterative Methods for Solving Fokker-Planck Equation

Hemeda

Eladdad

2018

Mathematical Problems in Engineering

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In this article, we propose the new iterative method and introduce the integral iterative method to solve linear and nonlinear Fokker-Planck equations and some similar equations. The results obtained by the two methods are compared with those obtained by both Adomian decomposition and variational iteration methods. Comparison shows that the two methods are more effective and convenient to use and overcome the difficulties arising in calculating Adomian polynomials and Lagrange multipliers, which means that the considered methods can simply and successfully be applied to a large class of problems.

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Section: Introductionmentioning

confidence: 99%

New Iterative Methods for Solving Fokker-Planck Equation

Hemeda

Eladdad

2018

Mathematical Problems in Engineering

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“…These equations are used to the modeling of transformation of pollutants, energy, subsurface water flows, deeper river flows, streams, and groundwater [4,11,12,19,23]. Recently, VO fractional diffusion equation is expanded to describe time-dependent anomalous diffusion and diffusion process in inhomogeneous porous media and for the description of complex dynamical problems [40].…”

Section: Introductionmentioning

confidence: 99%

A Hahn computational operational method for variable order fractional mobile–immobile advection–dispersion equation

2018

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In this paper, we consider the discrete Hahn polynomials fH n g and investigate their application for numerical solutions of the time fractional variable order mobile-immobile advection-dispersion model which is advantageous for modeling dynamical systems. This paper presented the operational matrix of derivative of discrete Hahn polynomials. The main advantage of approximating a continuous function by Hahn polynomials is that they have a spectral accuracy in the interval [0, N]. Furthermore, for computing the coefficients of the expansion uðxÞ ¼ P 1 n¼0 c n H n ðxÞ, we have to only compute a summation and the calculation of coefficients is exact. Also an upper bound for the error of the presented method, with equidistant nodes, is investigated. Illustrative examples are provided to show the accuracy and efficiency of the presented method. Using a small number of Hahn polynomials, significant results are achieved which are compared to other methods.

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“…The topic of integro-differential equations which are combination of differential and integral has attracted many scientists and researchers due to their applications in many areas; see, for example, [16,17] . Many mathematical formulation of physical phenomena contain integro-differential equations, and these equations may arise in fluid dynamics, biological models, and chemical kinetics; for more details, see [20,40] .…”

Section: Introductionmentioning

confidence: 99%

Study of Solution for a Parabolic Integrodifferential Equation with the Second Kind Integral Condition

2018

ijaa

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In this paper, we establish sufficient conditions for the existence, uniqueness and numerical solution for a parabolic integrodifferential equation with the second kind integral condition. The existence, uniqueness of a strong solution for the linear problem based on a priori estimate "energy inequality" and transformation of the linear problem to linear first-order ordinary differential equation with second member. Then by using a priori estimate and applying an iterative process based on results obtained for the linear problem, we prove the existence, uniqueness of the weak generalized solution of the integrodifferential problem. Also we have developed an efficient numerical scheme, which uses temporary problems with standard boundary conditions. A suitable combination of the auxiliary solutions defines an approximate solution to the original nonlocal problem, the algebraic matrices obtained after the full discretization are tridiagonal, then the solution is obtained by using the Thomas algorithm. Some numerical results are reported to show the efficiency and accuracy of the scheme.

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Application of Homotopy Perturbation and Variational Iteration Methods for Fredholm Integrodifferential Equation of Fractional Order

Cited by 14 publications

References 43 publications

New Iterative Methods for Solving Fokker-Planck Equation

New Iterative Methods for Solving Fokker-Planck Equation

A Hahn computational operational method for variable order fractional mobile–immobile advection–dispersion equation

Study of Solution for a Parabolic Integrodifferential Equation with the Second Kind Integral Condition

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