Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation
Analysis of PDEs
2025-05-19 v2 Numerical Analysis
Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2405.16841,
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 = {2025}
}