id: 02360925
dt: j
an: 2005d.01779
au: Fay, Temple H.; Joubert, Stephan V.
ti: Postanalysis of numerical solutions to ODEs.
so: N. Z. J. Math. 32, Suppl., 67-75 (2003).
py: 2003
pu: University of Auckland, Department of Mathematics, Auckland; New Zealand
Mathematical Society, Auckland
la: EN
cc: I75
ut:
ci:
li:
ab: Once one obtains a numerical solution to an ordinary differential equation,
how does one have confidence in this solution? Is it an approximation
to the exact solution or is it numeric rubbish? We give the reader two
simple procedures that can help raise one’s confidence levels. One is
based upon comparing solutions obtained at different precisions,
presumably, the higher the precision, the more accurate the solution.
The second simple procedure is that of calculating the residual
associated with the solution. Plots of the residual yield both global
and local information and can indicate where numerical difficulties
lie. We demonstrate this through the examination of known numerically
difficult examples. (Authors’ abstract)
rv: