Solution of the Third Kind Boundary Value Problem of Laplace’s Equation Based on Conformal Mapping

• 作者: Fuqian Wang
• 来源期刊: 应用数学与应用物理(英文)
• 学科: 数学
• 关键词: The THIRD KIND BOUNDARY Value Problem Laplace’s Equation CONFORMAL MAPPING The Electric Potential Distribution
• 年，卷（期）: 2019,（3）
• 页码范围: 536-546
• 页数: 11页
• 分类号: O1

摘要

In order to overcome the difficulty in solving the boundary value problem of electrostatic field with complex boundary and to give a new method for solving the third boundary value problem of Laplace’s equation, in this paper, the third boundary value problem of Laplace’s equation is studied by combining conformal mapping with theoretical analysis, the several analytical solutions of third boundary value problems of Laplace’s equation are gives, the correctness of its solution is verified through computer numerical simulation, and a new idea and method for solving the third boundary value problem of Laplace’s equation is obtained. In this paper, the boundary condition of the solving domain is changed by the appropriate conformal mapping, so that the boundary value problem on the transformed domain is easy to be solved or be known, and then the third kind boundary value of the Laplace’s equation can be solved easily;its electric potential distribution is known. Furthermore, the electric field line and equipotential line are plotted by using the MATLAB software.