The method of fundamental solutions for analytic functions in complex analysis

Abstract

<abstract><p>This paper extends the method of fundamental solutions (MFS) for solving the boundary value problems of analytic functions based on Cauchy-Riemann equations and properties of harmonic functions. The conformal mapping technique is applied to introduce the singularities of the approximate analytic functions and reconstruct the fundamental solutions. The presented method can naturally introduce the information of homogeneous boundary conditions and singularity properties, when the conformal mapping technique or the reconstructed fundamental solutions are used. The numerical examples show that the proposed method has the advantages of conciseness, reliability, efficiency, high accuracy and easy-using, respectively. The developed method can be used to solve the boundary value problems (BVPs) of analytic functions without considering single-valuedness, which simplify the numerical analysis.</p></abstract>