TITLE:
Solution of the Third Kind Boundary Value Problem of Laplace’s Equation Based on Conformal Mapping
AUTHORS:
Fuqian Wang
KEYWORDS:
The Third Kind Boundary Value Problem, Laplace’s Equation, Conformal Mapping, The Electric Potential Distribution
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.3,
March
14,
2019
ABSTRACT: 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.