The local Kansa׳s method for solving Berger equation. (August 2015)

• Record Type: Journal Article
• Authors: Yang, Jingyu; Liu, Xiaofeng; Wen, P.H.
• Is Part Of: Engineering analysis with boundary elements. Volume 57(2015:Aug.)
• Page Start: 16
• Page End: 22
• Publication Date: 2015-08
• Subjects: Berger equation -- RBF collocation methods -- Matern function -- MQ -- Shape parameter -- Local Kansa׳s method -- Leave-One-Out-Cross-Validation; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2015.03.005
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this paper, we present the local Kansa׳s method using radial basis functions (RBFs) to solve Berger equation which is a fourth order partial differential equation. To overcome the difficulty of solving higher order differential equations using localized RBF methods, we split the given equation into two second order partial differential equations. Furthermore, we use Matern function and normalized MQ as basis functions and make a comparison between the two radial basis functions in terms of accuracy and stability. LOOCV (Leave-One-Out-Cross-Validation) is used to find a good shape parameter of MQ and Matern function. To demonstrate the effectiveness of the local Kansa׳s method for solving Berger equation, three examples are given.