Finite integration method for solving multi-dimensional partial differential equations
نویسندگان
چکیده
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. Illustrative two-dimensional 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.
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