Arnold, A., & Körner, J. (2024). High-order WKB-based method for the 1D stationary Schrödinger equation in the semi-classical limit. In AIP Conference Proceedings (pp. 220002-1-220002–220004). AIP Publishing. https://doi.org/10.1063/5.0213306
We consider initial value problems for ε2 ϕ + a(x) ϕ = 0 in the highly oscillatory regime, i.e., with a(x) > 0 and
0 < ε 1. We discuss their efficient numerical integration on coarse grids, but still yielding accurate solutions. The O(h²) one-step method from [2] is based on an analytic WKB-preprocessing of the equation. Here we extend this method to O(h³) accuracy.
