Gaussian basis functions for solving differential equations

Authors

  • Andrew Gordon Allison
  • Derek Abbott
  • C. E. M. Pearce

DOI:

https://doi.org/10.21914/anziamj.v51i0.2630

Keywords:

Gaussian basis functions, differential equations, mesh-free methods, method of least-squares

Abstract

We derive approximate numerical solutions for an ordinary differential equation common in engineering using two different types of basis functions, polynomial and Gaussian, and a maximum discrepancy error measure. We compare speed and accuracy of the two solutions. The basic finding for our example is that while Gaussian basis functions can be used, the computational effort is greater than that required for a polynomial basis given the same degree of error.

Published

2010-10-26

Issue

Section

Proceedings Engineering Mathematics and Applications Conference