Highly Efficacious Sixth-Order Compact Approach with Nonclassical Boundary Specifications for the Heat Equation

This paper suggests an accurate numerical method based on a sixth-order compact difference scheme and explicit fourth-order Runge–Kutta approach for the heat equation with nonclassical boundary conditions (NCBC). According to this approach, the partial differential equation which represents the heat...

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Bibliographic Details
Published in:Mathematical problems in engineering 2022-12, Vol.2022, p.1-13
Main Authors: Arar, Nouria, Ait Kaki, Leila, Ben Makhlouf, Abdellatif
Format: Article
Language:English
Subjects:
Accuracy
Approximation
Boundary conditions
Boundary value problems
Exact solutions
Linear equations
Numerical methods
Ordinary differential equations
Partial differential equations
Runge-Kutta method
Thermodynamics
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Summary:This paper suggests an accurate numerical method based on a sixth-order compact difference scheme and explicit fourth-order Runge–Kutta approach for the heat equation with nonclassical boundary conditions (NCBC). According to this approach, the partial differential equation which represents the heat equation is transformed into several ordinary differential equations. The system of ordinary differential equations that are dependent on time is then solved using a fourth-order Runge–Kutta method. This study deals with four test problems in order to provide evidence for the accuracy of the employed method. After that, a comparison is done between numerical solutions obtained by the proposed method and the analytical solutions as well as the numerical solutions available in the literature. The proposed technique yields more accurate results than the existing numerical methods.
ISSN:1024-123X
1563-5147
DOI:10.1155/2022/8224959