Abstract
We present families of fourth-order mono-implicit Runge-Kutta-Nyström methods. Each member of these families can be considered as a modification of the Numerov method. Some parameters of these new methods are used to optimize the linear stability properties, i.e. to obtain P-stable methods with a minimal phase-lag. Also we show that in some cases there exist P-stable methods with stage-order 3. Since the methods considered are mono-implicit, the computational work needed in each time-step to solve the implicit equations is reduced seriously.
Research assistant of the University of Gent
Research Director at the National Fund for Scientific Research (N.F.W.O. Belgium)
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Van Hecke, T., Van Daele, M., Vanden Berghe, G., De Meyer, H., A mono-implicit Runge-Kutta-Nyström modification, of the Numerov method (to appear)
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© 1997 Springer-Verlag Berlin Heidelberg
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Van Hecke, T., Van Daele, M., Vanden Berghe, G., De Meyer, H. (1997). P-stable mono-implicit Runge-Kutta-Nyström modifications of the Numerov method. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_135
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DOI: https://doi.org/10.1007/3-540-62598-4_135
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