Fast Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinates

Shiferaw, Alemayehu; Mittal, R. C.

doi:10.4236/ajcm.2013.34045

Cited by 4 publications

(1 citation statement)

References 15 publications

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“…They extended the method to solve heat equation in two-dimensional with polar coordinates and threedimensional with cylindrical coordinates. Shiferaw and Mittal [11] solved three dimensional Poisson's equation with the finite difference method in cylindrical coordinates. Salehi and Granpayeh [12] presented a finite difference method for solving the two-dimensional Schrödinger equation in polar coordinates.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Three-Dimensional Transient Heat Conduction Equation in Cylindrical Coordinates

Tsega

2022

Journal of Applied Mathematics

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Heat equation is a partial differential equation used to describe the temperature distribution in a heat-conducting body. The implementation of a numerical solution method for heat equation can vary with the geometry of the body. In this study, a three-dimensional transient heat conduction equation was solved by approximating second-order spatial derivatives by five-point central differences in cylindrical coordinates. The stability condition of the numerical method was discussed. A MATLAB code was developed to implement the numerical method. An example was provided in order to demonstrate the method. The numerical solution by the method was in a good agreement with the exact solution for the example considered. The accuracy of the five-point central difference method was compared with that of the three-point central difference method in solving the heat equation in cylindrical coordinates. The solutions obtained by the numerical method in cylindrical coordinates were displayed in the Cartesian coordinate system graphically. The method requires relatively very small time steps for a given mesh spacing to avoid computational instability. The result of this study can provide insights to use appropriate coordinates and more accurate computational methods in solving physical problems described by partial differential equations.

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Section: Introductionmentioning

confidence: 99%