Work

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

Year: 2025

Type: article

Abstract: 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 the article (Arnold et al. SIAM J. Numer. Anal. 49, 1436–1460, 2011), we first analytically transform the given equation into a smoother (i.e., less oscillatory) equation. By developing sufficiently accurate quadratures for several (iterated) oscillatory integrals occurring in the Picard approximation of the solution, we obtain a one-step method that is third order w.r.t. the step size. The accuracy and efficiency of the method are illustrated through several numerical examples.

Source: Advances in Computational Mathematics

DOI: 10.1007/s10444-025-10234-y

Authors: Anton Arnold, Jannis Körner

Institution: TU Wien

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Austrian Science Fund, Technische Universität Wien