Luke Shaw

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math.NA2025

Polynomial Inequalities and Optimal Stability of Numerical Integrators

Luke Shaw

A numerical integrator for $x ˙ = f (x)$ is called \emph{stable} if, when applied to the 1D Dahlquist test equation $x ˙ = λ x, λ \in C$ with fixed timestep $h > 0$ , the nume…

math.NA2023

Generalized extrapolation methods based on compositions of a basic 2nd-order scheme

Sergio Blanes, Fernando Casas, Luke Shaw

We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differe…