Journal of Applied Mathematics & Bioinformatics

Analysis of Phase-lag for Diagonally Implicit Runge-Kutta-Nyström Methods

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• Abstract

  We analyse the phase errors introduced by diagonally implicit Runge-Kutta-Nystrom (DIRKN) methods when linear homogeneous test equation is integrated. It is shown that the homogeneous phase errors dominate if long interval integration are performed. Dispersion relations for the special class of DIRKN methods are derived and also both dissipative and zero-dissipative DIRKN methods are constructed. These methods are applied to linear differential equations with oscillating solutions and compared with the current of the same type DIRKN methods.