Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation
<|reference_start|>Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation: We present a framework for constructing a first-order hyperbolic system whose solution approximates that of a desired higher-order evolution equation. Constructions of this kind have received increasing interest in recent years, and are potentially useful as either analytical or computational tools for understanding the corresponding higher-order equation. We perform a systematic analysis of a family of linear model equations and show that for each member of this family there is a stable hyperbolic approximation whose solution converges to that of the model equation in a certain limit. We then show through several examples that this approach can be applied successfully to a very wide range of nonlinear PDEs of practical interest.<|reference_end|>
@article{ketcheson2024approximation,
    title={Approximation of arbitrarily high-order PDEs by first-order hyperbolic
  relaxation},
    author={David I. Ketcheson and Abhijit Biswas},
    journal={arXiv preprint arXiv:2405.16841},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.16841},
    primaryClass={math.AP cs.NA math.NA}
}