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arXiv · 2609.05939

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

Rahul Barthwal·Rahuldev Ghorai
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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.

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Rahul Barthwal, Rahuldev Ghorai. 2026-09-05. A structure-preserving implicit-explicit method for a hyperbolic approximation of fourth-order PDEs. https://arxiv.org/abs/2609.05939

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