Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation
Year: 2025
Type: article
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 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 partial differential equations of practical interest.
Source: Nonlinearity
Authors: David I Ketcheson, Abhijit Biswas
Institution: King Abdullah University of Science and Technology
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
OpenAlex ID: W4409370225