Symmetric-conjugate splitting methods for evolution equations of parabolic type

Sergio Blanes; Fernando Casas; Cesáreo González; Mechthild Thalhammer

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arXiv · 2401.04196

Symmetric-conjugate splitting methods for evolution equations of parabolic type

Sergio Blanes·Fernando Casas·Cesáreo González·Mechthild Thalhammer

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Abstract

The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant applications include nonreversible systems and ground state computations for linear Schr\"odinger equations based on the imaginary time propagation. Numerical examples confirm the favourable error behaviour of higher-order symmetric-conjugate splitting methods and illustrate the usefulness of a time stepsize control, where the local error estimation relies on the computation of the imaginary parts and thus requires negligible costs.

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Sergio Blanes, Fernando Casas, Cesáreo González, Mechthild Thalhammer. 2024-01-08. Symmetric-conjugate splitting methods for evolution equations of parabolic type. https://arxiv.org/abs/2401.04196

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