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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Absolute Stability<br />
For the linear equation<br />
u ′ (t) = Lu<br />
we say the solution is absolutely stable if |φ(λ∆t)| ≤ 1 for all λ ∈ σ(L).<br />
Example: Euler’s Method<br />
u n+1 = u n + ∆tF (u); φ(z) = 1 + z.<br />
−1<br />
D. Ketcheson (KAUST) 11 / 36
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