Homotopy Perturbation Method to Solve Heat Conduction Equation

Jawad, Anwar Ja'afar Mohamed

doi:10.5772/51509

Cited by 1 publication

(2 citation statements)

References 17 publications

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“…Makhtoumi [4] utilized the finite difference method to solve the heat equation, while Kafle et al [5] employed the same approach for a numerical study of parabolic PDEs. Iawad [6] opted for the perturbation method to numerically solve the heat equation. Butler and Kerr [7] provided a comprehensive introduction to various numerical techniques.…”

Section: Introductionmentioning

confidence: 99%

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Utilizing a third order difference scheme in numerical method of lines for solving the heat equation

Yaseen,

Batool

2024

Phys. Scr.

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Obtaining the numerical solution for partial differential equations (PDEs)is a fundamental task in computational mathematics and scientific computing. In this work, we propose a third order numerical method of lines (MOL) based on difference schemes for the efficient and accurate approximation of heat equation.The method combines the flexibility of MOL with the superior accuracy of higher order difference schemes. The proposed approach begins by discretizing the spatial domain, and then applies higher order difference schemes toapproximate the spatial derivatives in the PDE. The MOL framework is utilized to transform the resultant set of ordinary differential equations to a system of algebraic equations, facilitating their solution through an appropriate numerical method of choice. We have utilized the Adams method for this purpose. We analyze the stability of the proposed method and establish conditions under which it yields accurate and reliable solutions. We present the theoretical foundations of the method and discuss its implementation. We also present numerical results that demonstrate the procedure's precision and effectiveness. The results show that the method is able to achieve high accuracy with relatively few grid points, and the results are compared with those obtained by some existing numerical schemes accessible in the literature. 

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Section: Introductionmentioning

confidence: 99%

“…Smith [10] employed finite difference methods to solve various PDEs. Anwar [11] applied the homotopy perturbation method for the solution of heat conduction. Seena et al [12] presented a wavelet solution for one-dimensional heat conduction.…”

Section: Introductionmentioning

confidence: 99%

Utilizing a third order difference scheme in numerical method of lines for solving the heat equation

Yaseen,

Batool

2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

Homotopy Perturbation Method to Solve Heat Conduction Equation

Cited by 1 publication

References 17 publications

Utilizing a third order difference scheme in numerical method of lines for solving the heat equation

Utilizing a third order difference scheme in numerical method of lines for solving the heat equation

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