Gaussian basis functions for solving differential equations

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


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.


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

Full Text:



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.