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.
@article{2630,
title = {Gaussian basis functions for solving differential equations},
journal = {ANZIAM Journal},
volume = {51},
year = {2010},
doi = {10.21914/anziamj.v51i0.2630},
language = {EN},
url = {http://dml.mathdoc.fr/item/2630}
}
Allison, Andrew Gordon; Abbott, Derek; Pearce, C. E. M. Gaussian basis functions for solving differential equations. ANZIAM Journal, Tome 51 (2010) . doi : 10.21914/anziamj.v51i0.2630. http://gdmltest.u-ga.fr/item/2630/