Particular Solutions of Laplace and Bi-harmonic Operators Using Matern Radial Basis Functions
In this paper, we derive closed-form particular solutions of Matérn radial basis functions for the Laplace and biharmonic operator in 2D and Laplace operator in 3D. These derived particular solutions are essential for the implementation of the method of particular solutions for solving various types of partial differential equations. Four numerical examples in 2D and 3D are given to demonstrate the effectiveness of the derived particular solutions.
International Journal of Computer Mathematics
(2017). Particular Solutions of Laplace and Bi-harmonic Operators Using Matern Radial Basis Functions. International Journal of Computer Mathematics, 94(4), 690-706.
Available at: https://aquila.usm.edu/fac_pubs/17789