On the Linear Stability of Splitting Methods
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
On the Linear Stability of Splitting MethodsDate
2008Publisher
Springer VerlagISSN
16153375Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/acceptedVersionSubject
Abstract
A comprehensive linear stability analysis of splitting methods is carried out by means of a 2 × 2 matrix K(x) with polynomial entries (the stability
matrix) and the stability polynomial p(x) (the trace of K(x) divided ... [+]
A comprehensive linear stability analysis of splitting methods is carried out by means of a 2 × 2 matrix K(x) with polynomial entries (the stability
matrix) and the stability polynomial p(x) (the trace of K(x) divided by two).
An algorithm is provided for determining the coefficients of all possible time-
reversible splitting schemes for a prescribed stability polynomial. It is shown that p(x) carries essentially all the information needed to construct processed
splitting methods for numerically approximating the evolution of linear systems. By selecting conveniently the stability polynomial, new integrators with
processing for linear equations are built which are orders of magnitude more efficient than other algorithms previously available. [-]
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