Analysis On the Method of Fundamental Solutions for Biharmonic Equations

Authors

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

Document Type

Article

Publication Date

12-15-2018

Department

Mathematics

School

Mathematics and Natural Sciences

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.

Publication Title

Applied Mathematics and Computation

Volume

339

First Page

346

Last Page

366

Recommended Citation

Dou, F., Li, Z., Chen, C., Tian, Z. (2018). Analysis On the Method of Fundamental Solutions for Biharmonic Equations. Applied Mathematics and Computation, 339, 346-366.
Available at: https://aquila.usm.edu/fac_pubs/16961