IJPAM: Volume 42, No. 3 (2008)
A NONSTANDARD DIFFERENCE APPROACH FOR
A 2-DIMENSIONAL SINGULAR PERTURBATION PROBLEM
A 2-DIMENSIONAL SINGULAR PERTURBATION PROBLEM
F. Olcay Ilicasu
, David H. Schultz
Department of Mathematics
Rowan University
201 Mullica Hill Road, Glassboro, NJ 08028, USA
e-mail: ilicasu@rowan.edu
Department of Mathematical Sciences
University of Wisconsin - Milwaukee
P.O. Box 413, Milwaukee, WI 53211, USA
e-mail: schultz@uwm.edu
, David H. Schultz
Department of Mathematics
Rowan University
201 Mullica Hill Road, Glassboro, NJ 08028, USA
e-mail: ilicasu@rowan.edu
Department of Mathematical Sciences
University of Wisconsin - Milwaukee
P.O. Box 413, Milwaukee, WI 53211, USA
e-mail: schultz@uwm.edu
Abstract.We combine the two ideas of writing high order derivatives
coming from Taylor series expansions in terms of the lower order derivatives for a two dimensional test problem,
and rewriting the error of the expansions to reinforce diagonal dominance of the
resulting system. We develop two techniques using nine equally spaced points and
present numerical results.
Received: August 17, 2007
AMS Subject Classification: 65N06, 74H15, 74S20
Key Words and Phrases: high order derivatives, 2-dimensional singular perturbation problem, numerical results
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 3
