Advertisement
Published in:
01-10-2012
New Analysis of the Du Fort–Frankel Methods
Published in: Journal of Scientific Computing | Issue 1/2012
Log inActivate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Abstract
In 1953 Du Fort and Frankel (Math. Tables Other Aids Comput., 7(43):135–152, 1953) proposed to solve the heat equation u
t
=u
xx
using an explicit scheme, which they claim to be unconditionally stable, with a truncation error is of order of \(\tau= O({{k}}^{2}+{{h}}^{2}+\frac{{{k}}^{2}}{{{h}}^{2}})\). Therefore, it is not consistent when k=O(h).
In the analysis presented below we show that the Du Fort–Frankel schemes are not unconditionally stable. However, when properly defined, the truncation error vanishes as h,k→0.