Optimized High Order Explicit Runge-Kutta-Nyström Schemes

  • Marc DurufléEmail author
  • Mamadou N’diaye
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 119)


Runge-Kutta-Nyström (RKN) schemes have been developed to solve a non-linear ordinary differential equation (ODE) of the type y″ = f(t, y). In Chawla and Sharma (Computing, 26:247–256, 1981), the stability condition (the Courant-Friedrichs-Lewy or CFL) associated with these schemes have been studied for order 3, 4 and 5. In this paper, we extend this study for higher orders and we propose a new algorithm to compute numerically the CFL. By using this algorithm, we compute optimal coefficients for RKN schemes of orders 6, 7, 8 and 10 which maximize the CFL. Herein, the obtained schemes are used to solve non-linear Maxwell’s equations in 1-D.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Magique-3DInria Centre de Recherche Bordeaux Sud-OuestTalenceFrance
  2. 2.Laboratoire de Mathématiques et leurs ApplicationsUniversity of Pau and Pays de L’AdourPauFrance

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