The Closed-Form Particular Solutions For Laplace and Biharmonic Operators Using a Gaussian Function

Authors

A. R. Lamichhane, University of Southern Mississippi
C. S. Chen, University of Southern MississippiFollow

Document Type

Article

Publication Date

8-1-2015

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

Particular solutions play a critical role in solving inhomogeneous problems using boundary methods such as boundary element methods or boundary meshless methods. In this short article, we derive the closed-form particular solutions for the Laplace and biharmonic operators using the Gaussian radial basis function. The derived particular solutions are implemented numerically to solve boundary value problems using the method of particular solutions and the localized method of approximate particular solutions. Two examples in 2D and 3D are given to show the effectiveness of the derived particular solutions.

Publication Title

Applied Mathematics Letters

Volume

46

First Page

50

Last Page

56

Recommended Citation

Lamichhane, A., Chen, C. (2015). The Closed-Form Particular Solutions For Laplace and Biharmonic Operators Using a Gaussian Function. Applied Mathematics Letters, 46, 50-56.
Available at: https://aquila.usm.edu/fac_pubs/18585