
02360925
j
2005d.01779
Fay, Temple H.
Joubert, Stephan V.
Postanalysis of numerical solutions to ODEs.
N. Z. J. Math. 32, Suppl., 6775 (2003).
2003
University of Auckland, Department of Mathematics, Auckland; New Zealand Mathematical Society, Auckland
EN
I75
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)