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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{barthwal2026structurepreserving,
  title = {{A structure-preserving implicit-explicit method for a hyperbolic approximation of fourth-order PDEs}},
  author = {Rahul Barthwal and Rahuldev Ghorai},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05939},
  eprint = {2609.05939},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05939},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A structure-preserving implicit-explicit method for a hyperbolic approximation of fourth-order PDEs
AU  - Rahul Barthwal
AU  - Rahuldev Ghorai
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.05939
UR  - https://arxiv.org/abs/2609.05939
AB  - 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.
ER  -