Work

A structure-preserving implicit-explicit method for a hyperbolic approximation of fourth-order PDEs

Year: 2026

Type: preprint

Abstract: We introduce a novel structure-preserving numerical method for a first-order hyperbolic approximation system, which approximates the solutions of general fourth-order partial differential equations. By employing an implicit-explicit (IMEX) splitting between the stiff and non-stiff terms, we rigorously prove that the proposed scheme is energy-consistent and positivity-preserving under a CFL-type condition. Furthermore, we show that the method remains robustly stable in asymptotic regimes, with a time-step restriction that is entirely independent of the relaxation parameters. Finally, we present a series of numerical examples for thin film equations to validate the theoretical properties and efficacy of the scheme.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.05939

Authors: Barthwal, Rahul, Ghorai, Rahuldev

Institutions: University of Stuttgart, Centre National de la Recherche Scientifique, Institut de Recherche Mathématique Avancée, Université de Strasbourg

Language: English

Topic: Numerical Solvers for Ordinary Differential Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7212066997

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