Improved finite integration method for partial differential equations
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Volume
64
Pagination
230 - 236
Publisher
DOI
10.1016/j.enganabound.2015.12.012
Journal
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
ISSN
0955-7997
Metadata
Show full item recordAbstract
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.