Finite Difference Method For Laplace Equation In Irregular Domain

Juarlin, Eko

doi:10.1088/1742-6596/1354/1/012021

Cited by 1 publication

(2 citation statements)

References 3 publications

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“…In this paper, two methods are used, analytically and numerically. In the analytical method, the Laplacian equation that represents the physical system is solved analytically, which referred to a similar process in [11][12][13] by some mathematical tool, whereas in the numerical method using FDTD (Finite Different Time Domain) analysis to solve the boundary value problem, with the similar algorithm to [15].…”

Section: Methodsmentioning

confidence: 99%

“…Two approaches can be used to analyze the distribution of electric and magnetic fields, namely the analytical and numerical methods. The analytical approach method is based on solving differential equations with standard techniques found in calculus and solving boundary conditions of the physical system [11][12][13][14]. The numerical approach method is based on a numerical solution using a computer program carried out iteratively until the required accuracy is obtained [15].…”

Section: Introductionmentioning

confidence: 99%

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The Results Comparison of Numerical and Analytical Methods for Electric Potential on Rectangular Pipes

Maulana,

Rizaldi,

Bustomi

2023

J. Phys.: Conf. Ser.

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Two methods can be used to solve the problem of electric potential distribution in a rectangular pipe: numerical and analytical. The analytical solution is obtained using the Laplace equation and the given boundary conditions to complete the solution in the form of a linear combination of sinusoidal and hyperbolic functions. While the numerical solution is obtained using the finite difference method in the Python programming language. The comparison between the analytical and numerical solutions shows that the two have a good fit. This can be seen from the graph of the electric potential distribution in the rectangular pipe produced by the two methods. Numerical solutions obtained using the finite difference method in the Python programming language provide accurate and efficient results in solving the problem of the electric potential distribution in rectangular pipes. The use of the first four terms in the analytical method and the selection of 4 observation points on the pipe, namely points A (3.33, 1.67), B (3.33, 3.34), C (6.67, 1.67), and D (6.67, 3.34) produces a difference in the electric potential value between analytical and numerical methods each point is 35.91%, 51.96%, 51.96%, and 35.91%. The value difference between analytical and numerical methods will be smaller if more terms are taken in the analytical calculation, and more observation points are considered on the pipe.

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