Finite integration method for solving multi-dimensional partial differential equations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

16 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)4979-4994
Journal / PublicationApplied Mathematical Modelling
Volume39
Issue number17
Online published23 Apr 2015
Publication statusPublished - 1 Sep 2015

Abstract

Based on the recently developed Finite Integration Method (FIM) for solving one-dimensional ordinary and partial differential equations, this paper extends the technique to higher dimensional partial differential equations. The main idea is to extend the first order finite integration matrices constructed by using either Ordinary Linear Approach (OLA) (uniform distribution of nodes) or Radial Basis Function (RBF) interpolation (uniform/random distributions of nodes) to higher order integration matrices. Using standard time integration techniques, such as Laplace transform, we have shown that the FIM is capable for solving time-dependent partial differential equations. Illustrative numerical examples are given in two-dimension to compare the FIM (FIM-OLA and FIM-RBF) with the finite difference method and point collocation method to demonstrate its superior accuracy and efficiency.

Research Area(s)

  • Finite integration method, Laplace transformation, Partial differential equation, Radial basis functions, Wave equation