The Application of Bessel Function in the Definite Solution Problem of Cylindrical Coordinate System
Applied and Computational Mathematics
Volume 8, Issue 3, June 2019, Pages: 58-64
Received: Jul. 12, 2019; Accepted: Aug. 10, 2019; Published: Aug. 23, 2019
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Authors
Wenjie He, School of Mathematics and Physics, North China Electric Power University, Baoding, China
Meiling Zhao, School of Mathematics and Physics, North China Electric Power University, Baoding, China
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Abstract
The variable separation method is an important method to solve the definite solution problems, especially the definite solution problems of cylinder and sphere regions. This method can solve these problems on cylinder and sphere regions, but the solving procedures are very difficult in the practical application. It is often solved by combining the properties of Bessel functions. In this paper, we propose a method combining Bessel function to solve homogeneous definite solution problem on the cylindrical coordinate system and give the algorithm of solving a definite problem. This algorithm is easy to implement and simplifies the process of calculation. Firstly, the definition and properties of Bessel function are briefly recalled, which are the first and essential step to solve the definite solution problem. Then we give the basic process of solving homogeneous definite solution problem, where consider the problem of the definite solution of the homogeneous wave equation, homogeneous heat conduction equation and Laplace equation. We analyze the solution of the Bessel equation definite solution problem under three kinds of boundary conditions and conclude the algorithm of solving a definite problem. At last, two numerical examples are provided to validate the feasibility of the proposed method.
Keywords
Bessel Function, Definite Solution Problems, Cylindrical Coordinate
To cite this article
Wenjie He, Meiling Zhao, The Application of Bessel Function in the Definite Solution Problem of Cylindrical Coordinate System, Applied and Computational Mathematics. Vol. 8, No. 3, 2019, pp. 58-64. doi: 10.11648/j.acm.20190803.12
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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