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On the Convergence of Split Exponential Integrators for Semilinear Parabolic Problems

Year: 2026

Type: article

Abstract: . Splitting the exponential-like [Formula: see text] functions, which typically appear in exponential integrators, is attractive in many situations since it can dramatically reduce the computational cost of the procedure. However, depending on the employed splitting, this can result in order reduction. The aim of this paper is to analyze different such split approximations. We perform the analysis for semilinear problems in the abstract framework of commuting semigroups and derive error bounds that depend, in particular, on whether the vector (to which the [Formula: see text] functions are applied) satisfies appropriate boundary conditions. We then present the convergence analysis for two split versions of a second-order exponential Runge–Kutta integrator in the context of analytic semigroups, and show that one suffers from order reduction while the other does not. Numerical results for semidiscretized parabolic PDEs confirm the theoretical findings.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/25m1743454

Authors: Marco Caliari, Fabio Cassini, Lukas Einkemmer, Alexander Ostermann

Institutions: University of Verona, University of Padua, Universität Innsbruck

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per il Calcolo Scientifico

OpenAlex ID: W4415288844

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