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math.NA2024★ 5 cited
Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation
Abhijit Biswas, David I. Ketcheson, Hendrik Ranocha +1
We study the recently-proposed hyperbolic approximation of the Korteweg-de Vries equation (KdV). We show that this approximation, which we call KdVH, possesses a rich variety of so…
math.AP2024★ 4 cited
Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation
David I. Ketcheson, Abhijit Biswas
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 ha…