Optimized High Order Explicit Runge-Kutta-Nyström Schemes

Abstract : 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 [4], 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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  • HAL Id : hal-01403338, version 2

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Marc Durufle, Mamadou N'Diaye. Optimized High Order Explicit Runge-Kutta-Nyström Schemes. ICOSAHOM 2016 - International Conference on Spectral and High-Order Methods, Jun 2016, Rio de Janeiro, Brazil. pp.599-612. ⟨hal-01403338v2⟩

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