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arXiv · 2610.04355

Operator splitting methods for non-autonomous evolution equations comprising three parts, with application to the Bloch-Torrey equation of MRI

Barbara Kaltenbacher·Pablo Muñoz·Mechthild Thalhammer
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Abstract

In this paper we devise and analyze Lie Trotter splitting schemes for non-autonomous evolution equations, following two approaches: 1) A fully non-autonomous scheme, motivated by the potential use of explicit solutions of some subproblems. 2) A splitting scheme relying on the concept of Magnus integrators, where we freeze the operators at the beginning of each time interval as this suffices for first order convergence of the Lie-Trotter integrator. We derive first order convergence in a general setting and apply the analysis to the Bloch-Torrey equation of magnetic resonance imaging, where a decomposition into three subproblems is well-motivated by the physical role of the underlying operators. Numerical tests, complementing the time stepping scheme by a finite element space discretization, illustrate the theoretical findings.

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Barbara Kaltenbacher, Pablo Muñoz, Mechthild Thalhammer. 2026-10-03. Operator splitting methods for non-autonomous evolution equations comprising three parts, with application to the Bloch-Torrey equation of MRI. https://arxiv.org/abs/2610.04355

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