Finite Integration Method For Solving Multi-Dimensional Partial Differential Equations

Document Type

Article

Publication Date

1-1-2015

Department

Mathematics

School

Mathematics and Natural Sciences

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.

Publication Title

Applied Mathematical Modelling

Volume

39

Issue

17

First Page

4979

Last Page

4994

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