Title: Phase-fitted and amplification-fitted two-step hybrid methods for y '' = f (x, y)
Authors: Van de Vyver, Hans # ×
Issue Date: Dec-2007
Publisher: Elsevier
Series Title: Journal of Computational and Applied Mathematics vol:209 issue:1 pages:33-53
Abstract: This paper provides a theoretical framework for a new type of phase-fitted and amplification-fitted two-step hybrid (FTSH) methods which is introduced by the author in [H. Van de Vyver, A phase-fitted and amplification-fitted explicit two-step hybrid method for second-order periodic initial value problems, Internal. J. Modern Phys. C 17 (2006) 663-675]. The methods constitute a modification of dissipative two-step hybrid methods in the sense that two free parameters are added to eliminate the phase-lag and the amplification error. The methods are useful only when a good estimate of the frequency of the problem is known in advance. The parameters depend on the product of the estimated frequency and the stepsize. The algebraic order, zero-stability, stability and phase properties are examined. The theory is illustrated with sixth-order explicit FTSH methods. Numerical results carried out on an assortment of test problems show the relevance of the theory.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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