Computability of magnetic Schrödinger and Hartree equations on unbounded domains

Simon Becker, Jonathan Sewell, Euan Tebbutt

Research output: Contribution to journalArticlepeer-review

Abstract

We study the computability of global solutions to linear Schrödinger equations with magnetic fields and the Hartree equation on (Formula presented.). We show that the solution can always be globally computed with error control on the entire space if there exist a priori decay estimates in generalized Sobolev norms on the initial state. Using weighted Sobolev norm estimates, we show that the solution can be computed with uniform computational runtime with respect to initial states and potentials. We finally study applications in optimal control theory and provide numerical examples.

Original languageEnglish
JournalNumerical Methods for Partial Differential Equations
Early online date3 Oct 2022
DOIs
Publication statusE-pub ahead of print - 3 Oct 2022

Keywords

  • Hartree equation
  • Schrödinger equation
  • unbounded domains

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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