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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Spectral-fractional step Runge-Kutta discretizations for initial boundary value problems with time dependent boundary conditions


Authors: I. Alonso-Mallo, B. Cano and J. C. Jorge
Journal: Math. Comp. 73 (2004), 1801-1825
MSC (2000): Primary 65M20, 65M12; Secondary 65M60, 65J10
Published electronically: April 20, 2004
MathSciNet review: 2059737
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Abstract: In this paper we develop a technique for avoiding the order reduction caused by nonconstant boundary conditions in the methods called splitting, alternating direction or, more generally, fractional step methods. Such methods can be viewed as the combination of a semidiscrete in time procedure with a special type of additive Runge-Kutta method, which is called the fractional step Runge-Kutta method, and a standard space discretization which can be of type finite differences, finite elements or spectral methods among others. Spectral methods have been chosen here to complete the analysis of convergence of a totally discrete scheme of this type of improved fractionary steps. The numerical experiences performed also show the increase of accuracy that this technique provides.


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Additional Information

I. Alonso-Mallo
Affiliation: Departamento de Matemática Aplicada y Computación, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid, Spain
Email: isaias@mac.uva.es

B. Cano
Affiliation: Departamento de Matemática Aplicada y Computación, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid, Spain
Email: bego@mac.uva.es

J. C. Jorge
Affiliation: Departamento de Matemática e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain
Email: jcjorge@unavarra.es

DOI: http://dx.doi.org/10.1090/S0025-5718-04-01660-6
PII: S 0025-5718(04)01660-6
Keywords: Order reduction, fractional step Runge--Kutta methods, method of lines, partial differential equations, initial boundary value problems.
Received by editor(s): November 20, 2001
Received by editor(s) in revised form: December 30, 2002
Published electronically: April 20, 2004
Additional Notes: The first and second authors have obtained financial support from MCYT BFM 2001-2013 and JCYL VA025/01.
The third author has obtained financial support from the projects DGES PB97-1013, BFM2000-0803, a project of Gobierno de Navarra and a project of Universidad de La Rioja.
Article copyright: © Copyright 2004 American Mathematical Society