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

 

Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems


Authors: M. P. Calvo and C. Palencia
Journal: Math. Comp. 71 (2002), 1529-1543
MSC (2000): Primary 65M12, 65M20
Published electronically: November 19, 2001
MathSciNet review: 1933043
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Abstract: A new strategy to avoid the order reduction of Runge-Kutta methods when integrating linear, autonomous, nonhomogeneous initial boundary value problems is presented. The solution is decomposed into two parts. One of them can be computed directly in terms of the data and the other satisfies an initial value problem without any order reduction. A numerical illustration is given. This idea applies to practical problems, where spatial discretization is also required, leading to the full order both in space and time.


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Additional Information

M. P. Calvo
Affiliation: Departamento de Matemática Aplicada y Computación, Universidad de Valladolid, Valladolid, Spain
Email: maripaz@mac.cie.uva.es

C. Palencia
Affiliation: Departamento de Matemática Aplicada y Computación, Universidad de Valladolid, Valladolid, Spain
Email: palencia@mac.cie.uva.es

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01362-X
PII: S 0025-5718(01)01362-X
Keywords: Abstract initial boundary value problems, Runge-Kutta, order reduction
Received by editor(s): January 14, 2000
Received by editor(s) in revised form: November 30, 2000
Published electronically: November 19, 2001
Additional Notes: This research has been supported by DGICYT under project PB95-705 and by Junta de Castilla y León under project VA36/98.
Article copyright: © Copyright 2001 American Mathematical Society