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On the Linear Stability of Splitting Methods

By Sergio Blanes, Fernando Casas and Ander Murua


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

Topics: Splitting methods, Linear stability, Processing technique, AMS Classificationn numbers: 65L05, 65L20, Programació lineal
Publisher: Springer Verlag
Year: 2008
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