Modified Homotopy Perturbation Method for Dolving Nonlinear PDAEs and its Applications in Nanoelectronics

Jafari, Maryam; Hosseini, Mohammad Mehdi; Mohyud‐Din, Syed Tauseef; Ghovatmand, M.

doi:10.1515/ijnsns.2010.11.12.1047

Cited by 5 publications

(1 citation statement)

References 18 publications

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“…On one side, DAEs problems are treated by using: Padé series [50], Adomian decomposition method [51], homotopy analysis method [52]. On the other side, PDAEs problems are solved by using: Variational Methods [53], Modified Homotopy Perturbation Method [54], variational iteration method [55], Differential Transform Method [56]. Moreover, in [39], some higher-index DAEs were solved by transforming them first to index-one systems before applying the HPM.…”

Section: Introductionmentioning

confidence: 99%

Solution Procedure for Systems of Partial Dierential-Algebraic Equations by NHPM and Laplace-Padé Resummation

Benhammouda¹,

Vázquez-Leal

Sarmiento-Reyes³

2014

BJMCS

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In this paper, we propose an efficient modification of a New Homotopy Perturbation Method (NHPM) to obtain approximate and exact analytical solutions of Partial Differential-Algebraic Equations (PDAEs). The NHPM is first applied to the PDAE to obtain the exact solution in convergent series form. To improve the solution obtained from NHPM's truncated series, a post-treatment combining Laplace transform and Padé approximant is proposed. This modified Laplace-Padé new homotopy perturbation method is shown to be effective and greatly improves NHPM's truncated series solutions in convergence rate, and often leads to the exact solution.Two problems are solved to demonstrate the efficiency of the method; the first one is a nonlinear index-one system with an integral term and the second one is a linear index-three system with variable coefficients.

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Section: Introductionmentioning

confidence: 99%

Solution Procedure for Systems of Partial Dierential-Algebraic Equations by NHPM and Laplace-Padé Resummation

Benhammouda¹,

Vázquez-Leal

Sarmiento-Reyes³

2014

BJMCS

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Fuzzy Fractional Vibration Equation of Large Membrane

2016

Fuzzy Arbitrary Order System

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A comparison between numerical methods for solving Fuzzy fractional differential equations

Khan¹,

Riaz²,

Razzaq³

2014

Nonlinear Engineering

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In this paper, numerical simulation of linear and nonlinear fuzzy initial value problems of fractional order has been done. A modi cation in the improved Euler's method for fuzzy fractional order is proposed and utilized. Also, the two component homotopy perturbation method also known as a modi ed homotopy perturbation method (MHPM) is employed to solve the considered problems. The results obtained from the considered techniques are compared. These methods are illustrated by solving several examples. E ciency and exactness of results worked out from MHPM is examined from the tables and comparatively it is found that MHPM is more accurate and closer to the exact solutions than the existing methods.

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Modified Homotopy Perturbation Method for Dolving Nonlinear PDAEs and its Applications in Nanoelectronics

Cited by 5 publications

References 18 publications

Solution Procedure for Systems of Partial Dierential-Algebraic Equations by NHPM and Laplace-Padé Resummation

Solution Procedure for Systems of Partial Dierential-Algebraic Equations by NHPM and Laplace-Padé Resummation

Fuzzy Fractional Vibration Equation of Large Membrane

A comparison between numerical methods for solving Fuzzy fractional differential equations

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