Improved finite integration method for partial differential equations. (March 2016)

• Record Type: Journal Article
• Authors: Li, M.; Tian, Z.L.; Hon, Y.C.; Chen, C.S.; Wen, P.H.
• Is Part Of: Engineering analysis with boundary elements. Volume 64(2016:Mar.)
• Page Start: 230
• Page End: 236
• Publication Date: 2016-03
• Subjects: Finite integration method -- Numerical quadrature -- Simpson׳s rule -- Cotes integral formula -- Lagrange interpolation; 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.2015.12.012
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: Based on the recently developed finite integration method (FIM) for solving one-dimensional partial differential equations by using the trapezoidal rule for numerical quadrature, we improve in this paper the FIM with an alternative extended Simpson׳s rule in which the Cotes and Lagrange formulas are used to determine the first order integral matrix. The improved one-dimensional FIM is then further extended to solve two-dimensional problems. Numerical comparison with the finite difference method and the FIM (Trapezoidal rule) are performed by several one- and two-dimensional real application including the Poisson type differential equations and plate bending problems. It has been shown that the newly revised FIM has made significant improvement in terms of accuracy compare without much sacrifice on the stability and efficiency.