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Second Conference on Numerical Analysis and Applications
June 11-15, 2000
University of Rousse
Rousse, Bulgaria |
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Organizers
Plamen Yalamov, Marcin Paprzycki, Lubin Vulkov
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Fractional Step Runge-Kutta methods for the resolution of two dimensional time dependent coefficient evolutive convection-diffusion problems
by
Blanca Bujanda
Departamento de Matemáticas y Computación. Universidad de La Rioja
Coauthors: J.C. Jorge (Universidad Pública de Navarra)
Fractional Step Runge--Kutta methods for the resolution of two
dimensional time dependent coefficient evolutive
convection--diffusion problems
Fractional Step Runge-Kutta methods for the resolution of two
dimensional time dependent coefficient evolutive
convection-diffusion problems
B. Bujanda 1, J.C. Jorge 2
1 Departamento de Matemáticas y Computación,
Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa
s/n, 26004 Logroño, Spain. email:
bbujanda@dmc.unirioja.es
2 Departamento de Matemática e Informática,
Universidad Pública de Navarra, Edificio Los Acebos, Campus
Arrosadía s/n, 31006 Pamplona, Spain.
email: jcjorge@unavarra.es
Abstract
In this paper we obtain a unconditional convergence
result in the numerical resolution of two dimensional parabolic
problems whose coefficients depend on time. Our total
discretization schemes are deduced by combining Fractionary Steps
Runge-Kutta methods and simple upwind schemes on rectangular
grids. Classically, a stability property called AN-stability has
been imposed to the corresponding time integrators, in order
obtain unconditional
convergence when they are combined with finite difference or finite element
space dicretizations to integrate numerically such problems.
We have proved, for FSRK methods, that the AN-stability, which is
a strongly restrictive property for the design of high order
methods, can be avoided, being the A-stability a sufficient
condition, if the time variation in the coefficients is smooth.
We develop an A-stable third order FSRK method, and present some
numerical tests that show their efficiency and robustness in the
numerical resolution of evolutionary convection-diffusion
problems, even in some singular perturbation cases, if some kind
of rectangular special meshes are used.
Keywords: Fractional Steps; Stability.
AMS Subject classification: 65J10, 65M12.
Date received: February 10, 2000
Copyright © 2000 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # caen-21.