ALTERNATE DIRECTIONS OF HIGH-ORDER APPLIE D TO REACTION-DIFFUSION

Authors
DESCOMBES S SCHATZMAN M
Citation
S. Descombes et M. Schatzman, ALTERNATE DIRECTIONS OF HIGH-ORDER APPLIE D TO REACTION-DIFFUSION, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 321(11), 1995, pp. 1521-1524
Citations number
7
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
321
Issue
11
Year of publication
1995
Pages
1521 - 1524
Database
ISI
SICI code
0764-4442(1995)321:11<1521:ADOHAD>2.0.ZU;2-N
Abstract
An alternate direction formula of order 4 is derived for the reaction- diffusion system u(t) - u(xx) = f(u), split into its linear and nonlin ear parts. Richardson extrapolation is applied to a Strang formula. Th e diffusion is spectrally discretized and integrated exactly in time. The reaction term is integrated via an explicit Runge-Kutta scheme of order 4. Experimentally, the method is unconditionnally stable. The co mparison between error and CPU time favors our scheme over the classic al scheme of order 2. The method is highly parallelizable.