The Homotopy Perturbation Method for Solving Singular Initial Value Problems

Yıldırım, Ahmet; Agirseven, Deniz

doi:10.1515/ijnsns.2009.10.2.235

Cited by 14 publications

(5 citation statements)

References 16 publications

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“…Consequently, efficient methods have been developed for deriving exact and numerical solutions for these governing equations. For this aim, we list several important methods: the variational iteration method [12], homotopy perturbation method [13,14], the ( G ′ G )-expansion method [15,16] and the Lie group analysis method [17]- [20]. Using the Lie symmetry method, we can determine solutions of PDEs.…”

Section: Introductionmentioning

confidence: 99%

Lie Symmetry and Exact Solution of Conformable Time Fractional Schamel-Korteweg-De Vries Equation

Kumar,

Bansal

2023

Preprint

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In this current study, a systematic investigation is performed to derive symmetry reductions of conformable time-fractional Schamel-KdV equation via the Lie symmetry method. Using the obtained Lie point symmetries of nonlinear FPDEs the symmetry reduction is generated and utilized for the reduction into an ordinary differential equation. Some solutions of the reduced fractional ODEs are found with two straightforward methods to consider its traveling wave solution and series solutions, respectively. The method consists of the solutions which are trigonometric, hyperbolic, and rational functions. Also, we presented some figures for the obtained explicit solutions. AMS Math Subject Classification. 35Q53, 76M60, 83C15, 35C07.

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Section: Introductionmentioning

confidence: 99%

Lie Symmetry and Exact Solution of Conformable Time Fractional Schamel-Korteweg-De Vries Equation

Kumar,

Bansal

2023

Preprint

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“…The homotopy perturbation method (HPM) was introduced by Ji-Huan He in 1999 [9] for solving differential and integral equations. The HPM is applied to algebraic equations [10], nonlinear reactiondiffusion-convection problem [11], singular boundary and initial value problems [12,13], nonlinear wave equations [14], and other modifications which can be seen in [15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method

Mohamed

Yousif

Hamza

2022

Abstract and Applied Analysis

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In this paper, we combine the Elzaki transform method (ETM) with the new homotopy perturbation method (NHPM) for the first time. This hybrid approach can solve initial value problems numerically and analytically, such as nonlinear fractional differential equations of various normal orders. The Elzaki transform method (ETM) is used to solve nonlinear fractional differential equations, and then the homotopy is applied to the transformed equation, which includes the beginning conditions. To obtain the solution to an equation, we use the inverse transforms of the Elzaki transform method (ETM). The initial conditions have a big impact on the equation’s result. We give three beginning value issues that were solved as precise or approximation solutions with high rigor to demonstrate the method’s power and correctness. It is clear that solving nonlinear partial differential equations with the crossbred approach is the best alternative.

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“…Yusufoglu (2009) solved a linear Fredholm type integro-differential equations with separable kernel. Javidi 2009 Yildirim and Agirseven (2009) solved the space-time fractional advection-dispersion equation. Recently, we have studied the general SIR model which is a system of DEs which are used as a mathematical model in physically significant field of applied science.…”

Section: Introductionmentioning

confidence: 99%

Application of Homotopy Perturbation Method for SIR Model with Vital Dynamics and Constant Population

Mechee¹,

Al-Juaifri²

2018

American Journal of Applied Sciences

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In this work, we have studied Susceptible-Infected-Recovered (SIR) model with vital dynamics and constant population, which is used as a mathematical models in many physically significant fields of applied science. The Homotopy Perturbation Method (HPM) and Runge-Kutta method (RK) have been used for solving the SIR model with vital dynamics and constant population. The convergence of HPM has been studied. Also, we have tested the HPM on solving different implementations which are show the efficiency and accuracy of the method. The approximated solutions of HPM for the tested problems are agree well with the numerical solutions of Runge-Kutta method.

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The Homotopy Perturbation Method for Solving Singular Initial Value Problems

Cited by 14 publications

References 16 publications

Lie Symmetry and Exact Solution of Conformable Time Fractional Schamel-Korteweg-De Vries Equation

Lie Symmetry and Exact Solution of Conformable Time Fractional Schamel-Korteweg-De Vries Equation

Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method

Application of Homotopy Perturbation Method for SIR Model with Vital Dynamics and Constant Population

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