Solution of the differential algebraic equations via homotopy perturbation method and their engineering applications

Soltanian, Fahimeh; Dehghan, Mehdi; Karbassi, S. M.

doi:10.1080/00207160802545908

Cited by 49 publications

(38 citation statements)

References 53 publications

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“…The HPM is modified in [57] by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equations, and so on. It is worth pointing out that this technique is used by authors of [58] to solve the differential algebraic equations.…”

Section: The Homotopy Perturbation Methodsmentioning

confidence: 99%

A seminumeric approach for solution of the Eikonal partial differential equation and its applications

Dehghan

Salehi

2009

Numerical Methods Partial

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In this work, a partial differential equation, which has several important applications, is investigated, and some techniques based on semianalytic (or quasi-numerical) approaches are developed to find its solution. In this article, the homotopy perturbation method (HPM), Adomian decomposition method, and the modified homotopy perturbation method are proposed to solve the Eikonal equation. HPM yields solution in convergent series form with easily computable terms, and in some case, yields exact solutions in one iteration. In other hand, in Adomian decomposition method, the approximate solution is considered as an infinite series usually converges to the accurate solution. Moreover, these methods do not require any discretization, linearization, or small perturbation, and therefore reduce the numerical computation a lot. Several test problems are given and results are compared with the variational iteration method.

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Section: The Homotopy Perturbation Methodsmentioning

confidence: 99%

A seminumeric approach for solution of the Eikonal partial differential equation and its applications

Dehghan

Salehi

2009

Numerical Methods Partial

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“…The homotopy perturbation method is used in [70] to solve a partial differential equation subject to temperature overspecification. This technique is employed in [71] to solve the differential-algebraic equations.…”

Section: B Homotopy Perturbation Methodsmentioning

confidence: 99%

The numerical solution of the second Painlevé equation

Dehghan

Shakeri

2009

Numerical Methods Partial

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The Painlevé equations were discovered by Painlevé, Gambier and their colleagues during studying a nonlinear second-order ordinary differential equation. The six equations which bear Painlevé's name are irreducible in the sense that their general solutions cannot be expressed in terms of known functions. Painlevé has derived these equations on the sole requirement that their solutions should be free from movable singularities. Many situations in mathematical physics reduce ultimately to Painlevé equations: applications including statistical mechanics, plasma physics, nonlinear waves, quantum gravity, quantum field theory, general relativity, nonlinear optics, and fiber optics. This fact has caused a significant interest to the study of these equations in recent years. In this study, the solution of the second Painlevé equation is investigated by means of Adomian decomposition method, homotopy perturbation method, and Legendre tau method. Then a numerical evaluation and comparison with the results obtained by the method of continuous analytic continuation are included.

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“…In recent years, many researchers have focused on the numerical solution of fractional differential -algebraic equations. Some numerical methods have been developed, such as implicit RungeKutta method [5], Padé approximation method [6][7][8][9], homotopy perturbation method [10][11][12][13][14], Adomian decomposition method [15][16][17][18][19], homotopy analysis method [20][21], variation iteration method [22][23][24], homotopy analysis transform method [25]. In 2013, Habibolla et al [26] presented an alternative approach based on Laplace iterative method (LIM) for finding series solutions to linear and nonlinear systems of PDEs.…”

Section: Introductionmentioning

confidence: 99%

An efficient scheme for solving a system of time- fractional order differential-algebraic equations by using fractional Laplace iteration method

Hasan

Namah

2016

IJAMS

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Solution of the differential algebraic equations via homotopy perturbation method and their engineering applications

Cited by 49 publications

References 53 publications

A seminumeric approach for solution of the Eikonal partial differential equation and its applications

A seminumeric approach for solution of the Eikonal partial differential equation and its applications

The numerical solution of the second Painlevé equation

An efficient scheme for solving a system of time- fractional order differential-algebraic equations by using fractional Laplace iteration method

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