9 citations · 22 across the 11 of their papers we have counts for
12 papers
Asymptotic-Preserving Exponential Integrators applied to the Hyperbolic Korteweg-de Vries System
Abhijit Biswas, Sebastiano Boscarino, David I. Ketcheson +1
We study the application of exponential time integration methods, coupled with Fourier pseudospectral space discretization, to the hyperbolic Korteweg-de Vries (KdVH) system. We in…
Adaptive Diagonally Implicit Runge-Kutta Methods Devoid of Order Reduction for Semilinear ODEs
Steven B. Roberts, Abhijit Biswas, David Shirokoff +1
Diagonally implicit Runge-Kutta (DIRK) methods are a prominent class of numerical methods for solving stiff systems of ordinary differential equations (ODEs). Stiffness does not on…
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…
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 str…
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…
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…
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…
Explicit Runge Kutta Methods that Alleviate Order Reduction
Abhijit Biswas, David I. Ketcheson, Steven Roberts +2
Explicit Runge--Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to initial-boundary value problem with time-dependent boundary c…
Accurate Solution of the Nonlinear Schrödinger Equation via Conservative Multiple-Relaxation ImEx Methods
Abhijit Biswas, David I. Ketcheson
The nonlinear Schrödinger (NLS) equation possesses an infinite hierarchy of conserved densities and the numerical preservation of some of these quantities is critical for accurate…
Multiple-Relaxation Runge Kutta Methods for Conservative Dynamical Systems
Abhijit Biswas, David I. Ketcheson
We generalize the idea of relaxation time stepping methods in order to preserve multiple nonlinear conserved quantities of a dynamical system by projecting along directions defined…
Design of DIRK Schemes with High Weak Stage Order
Abhijit Biswas, David Ketcheson, Benjamin Seibold +1
Runge-Kutta (RK) methods may exhibit order reduction when applied to certain stiff problems. While fully implicit RK schemes exist that avoid order reduction via high-stage order,…
Algebraic Structure of the Weak Stage Order Conditions for Runge-Kutta Methods
Abhijit Biswas, David Ketcheson, Benjamin Seibold +1
Runge-Kutta (RK) methods may exhibit order reduction when applied to stiff problems. For linear problems with time-independent operators, order reduction can be avoided if the meth…