Analysis of trigonometric implicit Runge-Kutta methods
Contribuinte(s) |
Brenner, S. Goovaerts, M. J. Mitsui, T. Ng, M. B Sommeijer Wuytack, L. |
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Data(s) |
01/01/2006
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Resumo |
Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge-Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge-Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. (c) 2006 Elsevier B.V. All rights reserved. |
Identificador | |
Idioma(s) |
eng |
Publicador |
Elsevier |
Palavras-Chave | #Mathematics, Applied #oscillatory ODEs #variable stepsize #variable coefficients #trigonometric collocation #implicit RK #Mixed Collocation Methods #Variable-coefficients #Nystrom Methods #Stability #C1 #230116 Numerical Analysis #780101 Mathematical sciences |
Tipo |
Journal Article |