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Efficient numerical method for highly oscillatory 1D Schrödinger equation

Published on:

28 February 2024

Primary Category:

Numerical Analysis

Paper Authors:

Anton Arnold,

Jannis Körner

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Key Details

Presents numerical method for highly oscillatory 1D Schrödinger equation

Analytically transforms equation into smoother form as preprocessing step

Develops one-step method using accurate quadratures for oscillatory integrals

Method is third order accurate with respect to step size

Efficiency and accuracy demonstrated through numerical examples

AI generated summary

Efficient numerical method for highly oscillatory 1D Schrödinger equation

This paper introduces a numerical method to efficiently solve the highly oscillatory 1D stationary Schrödinger equation by first analytically transforming it into a smoother equation. A one-step method is developed using accurate quadratures for oscillatory integrals in the solution's Picard approximation. The method is third order accurate and illustrated to be efficient and accurate through numerical examples.

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