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

✍ Scribed by H De Meyer; G Vanden Berghe; T Van Hecke; M Van Daele

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
1017 KB
Volume
87
Category
Article
ISSN
0377-0427

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✦ Synopsis

Mono-implicit Runge-Kutta methods can be used to generate implicit Runge-Kutta-Nystr6m (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-Nystr6m 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.

📜 SIMILAR VOLUMES

Deferred correction with mono-implicit R
Deferred correction with mono-implicit Runge–Kutta methods for first-order IVPs
✍ M.Van Daele; T.Van Hecke; G.Vanden Berghe; H.De Meyer 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 194 KB

To reach a high order of accuracy for numerical solutions of IVPs with mono-implicit Runge-Kutta (MIRK) methods, the technique of deferred correction is used. Special attention is paid to the possible increase of the order and the stability of such schemes. Several schemes are given.