Alexander H.D. Cheng talks
with ScienceWatch.com and answers a few questions
about this month's Fast Moving Front in the field of
Mathematics. The author has also sent along images of their
work.
Article: Exponential convergence and H-c
multiquadric collocation method for partial differential
equations
Authors:
Cheng,
AHD;Golberg, MA;Kansa, EJ;Zammito, G
Journal: NUMER METHOD PARTIAL DIFFER E, 19 (5): 571-594 SEP
2003
Addresses: Univ Mississippi, Dept Civil Engn, 203 Carrier
Hall,POB 1848, University, MS 38677 USA.
Univ Mississippi, Dept Civil Engn, University, MS 38677
USA.
Embry Riddle Aeronaut Univ, Oakland, CA 94621 USA.
(addresses have been truncated)
Figure 1: This figure shows that using a
finite difference method with a 100 x 100
grid, it delivers an accuracy of
10-4. Using the multiquadric
collocation method with a 20 x 20 grid, an
accuracy of 10-6 is
accomplished. In fact, later computation
(Huang, et al., 2007) delivered an
accuracy of 10-15 using the same
20 x 20 grid.
Figure
2:
Figure 2: This figure shows the simplicity
of the method: the top two equations are
the problem to be solved; the bottom three
equations are the methodology to solve
it.