Particular solutions of Laplace and bi-harmonic operators using Matérn radial basis functions. Issue 4 (3rd April 2017)

• Record Type: Journal Article
• Authors: Lamichhane, A. R.; Chen, C. S.
• Is Part Of: International journal of computer mathematics. Volume 94:Issue 4(2017)
• Page Start: 690
• Page End: 706
• Publication Date: 2017-04-03
• Subjects: Radial basis functions -- Matérn function -- the method of particular solutions; 65Y40 -- 68W05; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2015.1127359
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: 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.