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On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods

Hans De Meyer (UGent), Guido Vanden Berghe (UGent), Tanja Van Hecke (UGent) and Marnix Van Daele (UGent)
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Abstract
Mono-implicit Runge-Kutta methods can be used to generate implicit Runge-Kutta-Nystrom (IRKN) methods for the numerical solution of systems of second-order differential equations. The paper is concerned with the investigation of the conditions to be fulfilled by the mono-implicit Runge-Kutta (MIRK) method in order to generate a mono-implicit Runge-Kutta-Nystrom method (MIRKN) that is P-stable. One of the main theoretical results is the property that MIRK methods (in standard form) cannot generate MIRKN methods (in standard form) of order greater than 4. Many examples of MIRKN methods generated by MIRK methods are presented.
Keywords
Runge-Kutta methods, ODE, Runge-Kutta-Nystrom methods, mono-implicit Runge-Kutta (Nystrom) methods, P-stability, INITIAL-VALUE-PROBLEMS, ONE-STEP METHODS, ORDINARY DIFFERENTIAL-EQUATIONS, P-STABLE METHODS, NUMERICAL-SOLUTION, ODES, INTEGRATION, STABILITY, FORMULAS, SYSTEMS

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Chicago
De Meyer, Hans, Guido Vanden Berghe, Tanja Van Hecke, and Marnix Van Daele. 1997. “On the Generation of Mono-implicit Runge-Kutta-Nyström Methods by Mono-implicit Runge-Kutta Methods.” Journal of Computational and Applied Mathematics 87 (1): 147–167.
APA
De Meyer, Hans, Vanden Berghe, G., Van Hecke, T., & Van Daele, M. (1997). On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 87(1), 147–167.
Vancouver
1.
De Meyer H, Vanden Berghe G, Van Hecke T, Van Daele M. On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 1997;87(1):147–67.
MLA
De Meyer, Hans, Guido Vanden Berghe, Tanja Van Hecke, et al. “On the Generation of Mono-implicit Runge-Kutta-Nyström Methods by Mono-implicit Runge-Kutta Methods.” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 87.1 (1997): 147–167. Print.
@article{176186,
  abstract     = {Mono-implicit Runge-Kutta methods can be used to generate implicit Runge-Kutta-Nystrom (IRKN) methods for the numerical solution of systems of second-order differential equations. The paper is concerned with the investigation of the conditions to be fulfilled by the mono-implicit Runge-Kutta (MIRK) method in order to generate a mono-implicit Runge-Kutta-Nystrom method (MIRKN) that is P-stable. One of the main theoretical results is the property that MIRK methods (in standard form) cannot generate MIRKN methods (in standard form) of order greater than 4. Many examples of MIRKN methods generated by MIRK methods are presented.},
  author       = {De Meyer, Hans and Vanden Berghe, Guido and Van Hecke, Tanja and Van Daele, Marnix},
  issn         = {0377-0427},
  journal      = {JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS},
  keyword      = {Runge-Kutta methods,ODE,Runge-Kutta-Nystrom methods,mono-implicit Runge-Kutta (Nystrom) methods,P-stability,INITIAL-VALUE-PROBLEMS,ONE-STEP METHODS,ORDINARY DIFFERENTIAL-EQUATIONS,P-STABLE METHODS,NUMERICAL-SOLUTION,ODES,INTEGRATION,STABILITY,FORMULAS,SYSTEMS},
  language     = {eng},
  number       = {1},
  pages        = {147--167},
  title        = {On the generation of mono-implicit Runge-Kutta-Nystr{\"o}m methods by mono-implicit Runge-Kutta methods},
  url          = {http://dx.doi.org/10.1016/S0377-0427(97)00183-0},
  volume       = {87},
  year         = {1997},
}

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