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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<strong>Runge</strong>-<strong>Kutta</strong> Methods<br />
To solve the initial value problem:<br />
u ′ (t) = F (u(t)), u(0) = u 0<br />
a <strong>Runge</strong>-<strong>Kutta</strong> method computes approximations u n ≈ u(n∆t):<br />
�<br />
y i = u n i−1<br />
+ ∆t aijF (y j )<br />
j=1<br />
u n+1 = u n s−1<br />
+ ∆t<br />
�<br />
bjF (y j )<br />
The accuracy and stability <strong>of</strong> the method depend on the coefficient matrix<br />
A and vector b.<br />
j=1<br />
D. Ketcheson (KAUST) 7 / 36
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