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5 papers
A Stiff Order Condition Theory for Runge-Kutta Methods Applied to Semilinear ODEs
Steven B. Roberts, David Shirokoff, Abhijit Biswas +1
Classical convergence theory of Runge-Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE). For stiff pr…
Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation
Sebastian Bleecke, Abhijit Biswas, David I. Ketcheson +2
We study the hyperbolic approximation of the Benjamin-Bona-Mahony (BBM) equation proposed recently by Gavrilyuk and Shyue (2022). We develop asymptotic-preserving numerical methods…
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…
A Hyperbolic Approximation of the Nonlinear Schrödinger Equation
Abhijit Biswas, Laila S. Busaleh, David I. Ketcheson +2
We study a first-order hyperbolic approximation of the nonlinear Schrödinger (NLS) equation. We show that the system is strictly hyperbolic and possesses a modified Hamiltonian st…
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…