Analysis On the Method of Fundamental Solutions for Biharmonic Equations

Fangfang Dou, University of Electronic Science and Technology of China
Zi-Cai Li, National Sun Yat-sen University
Ching-Shyang Chen, University of Southern Mississippi
Zhaolu Tian, Taiyuan University of Technology

Abstract

In this paper, the error and stability analysis of the method of fundamental solution (MFS) is explored for biharmonic equations. The bounds of errors are derived for the fundamental solutions r²ln r in bounded simply-connected domains, and the polynomial convergence rates are obtained for certain smooth solutions. The bounds of condition number are also derived to show the exponential growth rates for disk domains. Numerical experiments are carried out to support the above analysis, which is the first time to provide the rigorous analysis of the MFS using r²ln r for biharmonic equations.