Design of optimal Runge-Kutta methods - FEniCS Project
Design of optimal Runge-Kutta methods - FEniCS Project
Design of optimal Runge-Kutta methods - FEniCS Project
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Nonlinear accuracy<br />
Besides the conditions on the stability polynomial coefficients, high order<br />
<strong>Runge</strong>-<strong>Kutta</strong> <strong>methods</strong> must satisfy additional nonlinear order conditions.<br />
p = 1: �<br />
i bi = 1<br />
p = 2: �<br />
i,j biaij = 1/2<br />
p = 3: �<br />
i,j,k biaijajk �<br />
= 1/6<br />
i,j,k biaijaik = 1/3<br />
Number <strong>of</strong> conditions grows factorially (719 conditions for order 10).<br />
D. Ketcheson (KAUST) 20 / 36
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