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Research Article | Open Access

The shift-based scaling and recursing algorithm for evaluating the action of the matrix φ-functions

Xianan Lu, Dongping Li( ), Zhixin Zhao( )
School of Mathematics, Changchun Normal University, 677 Changji North Road, Changchun, MO 130032, China
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Abstract

In this paper, we present an efficient method for computing the action of matrix φ-functions. Our approach is based on a scaling and recursing procedure and incorporates a shifting technique as a preprocessing step to enhance efficiency. We conduct a forward error analysis to determine the optimal scaling parameter and polynomial degree for achieving the desired accuracy. Numerical comparisons with existing algorithms demonstrate that the proposed algorithm performs well in terms of both accuracy and efficiency.

Keywords

φ-functionsscaling and recursing methodshifting techniqueTaylor seriesforward error analysisexponential integrators
CLC number: 65L05, 65F10, 65F30

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AIMS Mathematics
Volume 10 Issue 2,
February 2025
Pages 2854-2868
DOI: 10.3934/math.2025133

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Cite this article:
Lu X, Li D, Zhao Z. The shift-based scaling and recursing algorithm for evaluating the action of the matrix φ-functions. AIMS Mathematics, 2025, 10(2): 2854-2868. https://doi.org/10.3934/math.2025133

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Received: 09 November 2024
Revised: 21 January 2025
Accepted: 05 February 2025
Published: 15 February 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)