A multiple-scale Pascal polynomial triangle solving elliptic equations and inverse Cauchy problems. (January 2016)

• Record Type: Journal Article
• Authors: Liu, Chein-Shan; Kuo, Chung-Lun
• Is Part Of: Engineering analysis with boundary elements. Volume 62(2016:Jan.)
• Page Start: 35
• Page End: 43
• Publication Date: 2016-01
• Subjects: Multi-scale polynomial expansion -- Pascal triangle -- Elliptic PDEs -- Inverse Cauchy problems; 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.2015.09.003
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: The polynomial expansion method is a useful tool to solve partial differential equations (PDEs). However, the researchers seldom use it as a major medium to solve PDEs due to its highly ill-conditioned behavior. We propose a single-scale and a multiple-scale Pascal triangle formulations to solve the linear elliptic PDEs in a simply connected domain equipped with complex boundary shape. For the former method a constant parameter R 0 is required, while in the latter one all introduced scales are automatically determined by the collocation points. Then we use the multiple-scale method to solve the inverse Cauchy problems, which is very accurate and very stable against large noise to 20%. Numerical results confirm the validity of the present multiple-scale Pascal polynomial expansion method.