Jannis Körner

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math.NA2024

WKB-based third order method for the highly oscillatory 1D stationary Schrödinger equation

Anton Arnold, Jannis Körner

This paper introduces an efficient high-order numerical method for solving the 1D stationary Schrödinger equation in the highly oscillatory regime. Building upon the ideas from [Ar…

math.NA2024

Optimally truncated WKB approximation for the 1D stationary Schrödinger equation in the highly oscillatory regime

Anton Arnold, Christian Klein, Jannis Körner +1

This paper is dedicated to the efficient numerical computation of solutions to the 1D stationary Schrödinger equation in the highly oscillatory regime. We compute an approximate so…

math.NA2023

High-order WKB-based Method For The 1D Stationary Schrödinger Equation In The Semi-classical Limit

Anton Arnold, Jannis Körner

We consider initial value problems for $ε^{2} φ^{''} + a (x) φ = 0$ in the highly oscillatory regime, i.e., with $a (x) > 0$ and $0 < ε ≪ 1$ . We discuss their efficient num…

math.NA2023

Optimally truncated WKB approximation for the highly oscillatory stationary 1D Schrödinger equation

Jannis Körner, Anton Arnold, Christian Klein +1

We discuss the numerical solution of initial value problems for $ε^{2} φ^{''} + a (x) φ = 0$ in the highly oscillatory regime, i.e., with $a (x) > 0$ and $0 < ε ≪ 1$ . We an…