A P-stable singly diagonally implicit Runge–Kutta–Nyström method |
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Authors: | G. Papageorgiou I.Th. Famelis Ch. Tsitouras |
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Affiliation: | (1) Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece |
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Abstract: | A five-stage fifth-order singly diagonally implicit Runge–Kutta–Nyström method for the integration of second order differential equations possessing an oscillatory solution, is presented in this article. This method is P-stable, which is recommended for problems with a theoretical solution consisting of a periodic part of moderate frequency with a high frequency oscillation with small amplitude superimposed. It also attains an order which is one higher than existing methods of this type. Numerical comparisons with existing methods of this type show its clear advantage. |
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Keywords: | P-stability singly diagonally implicit Runge– Kutta– Nystr?m 65L05 65L06 65L20 |
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