134 citations · 770 across the 68 of their papers we have counts for
73 papers
Optimized linear multistep methods for stiff problems
Tyler Jensen, David I Ketcheson, Lajos Lóczi
We design and test several new optimized linear multistep methods for stiff problems. Each method is A-stable, implicit, and second-order accurate. We focus on achieving the smalle…
Compartmental epidemiological models with infection-driven immune escape
Daniela R. Ramírez-Gutiérrez, Lajos Lóczi, Carlos Muñoz-Moncayo +1
We propose and study a compartmental epidemiological model that incorporates both waning immunity and mutation-driven immune escape into a single-strain framework. The model, terme…
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, efficient, and scalable water wave modeling with dispersive hyperbolic systems
Carlos Muñoz-Moncayo, David I. Ketcheson
Accurate modeling of tsunamis (such as those generated by landslides) requires capturing both wave dispersion in the deep ocean and wave breaking near the shore. The shallow water…
Efficient High-order Mass-conserving and Energy-balancing Schemes for Schrödinger-Poisson Equations
Manvendra Pratap Rajvanshi, David I. Ketcheson
We study relaxation-based approaches for conserving mass and energy in the numerical solution of Schrödinger-Poisson (SP) type systems. Relaxation-based methods offer a general app…
Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schrödinger equations
Hendrik Ranocha, David I. Ketcheson
We propose and study a class of arbitrarily high-order numerical discretizations that preserve multiple invariants and are essentially explicit (they do not require the solution of…
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…
High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation and its hyperbolization
Hendrik Ranocha, David I. Ketcheson
We propose a class of numerical methods for the nonlinear Schrödinger (NLS) equation that conserves mass and energy, is of arbitrarily high-order accuracy in space and time, and re…
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…
Solitary wave formation in the compressible Euler equations
David I. Ketcheson, Giovanni Russo
We study the behavior of perturbations in a compressible one-dimensional inviscid gas with an ambient state consisting of constant pressure and periodically-varying density. We sho…
Homogenized Equations for Isentropic Gas in a Pipe with Periodically-Varying Cross-Section
Laila S. Busaleh, David I. Ketcheson
We analyze the behavior of an isentropic gas in a narrow pipe with periodically-varying cross-sectional area. Using multiple-scale perturbation theory, we derive homogenized effect…
A dispersive effective equation for transverse propagation of planar shallow water waves over periodic bathymetry
David I. Ketcheson, Giovanni Russo
We study the behavior of shallow water waves propagating over bathymetry that varies periodically in one direction and is constant in the other. Plane waves traveling along the con…
Pseudo-Energy-Preserving Explicit Runge-Kutta Methods
Gabriel A. Barrios de León, David I. Ketcheson, Hendrik Ranocha
Using a recent characterization of energy-preserving B-series, we derive the explicit conditions on the coefficients of a Runge-Kutta method that ensure energy preservation (for Ha…
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…
A multiscale model for weakly nonlinear shallow water waves over periodic bathymetry
David I. Ketcheson, Lajos Lóczi, Giovanni Russo
We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are…
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…
A high-order finite volume method for Maxwell's equations in heterogeneous and time-varying media
Damian P. San Roman Alerigi, David I. Ketcheson, Boon S. Ooi
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservativ…
Order conditions for Runge--Kutta-like methods with solution-dependent coefficients
Thomas Izgin, David I. Ketcheson, Andreas Meister
In recent years, many positivity-preserving schemes for initial value problems have been constructed by modifying a Runge--Kutta (RK) method by weighting the right-hand side of the…
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…
Very High-Order A-stable Stiffly Accurate Diagonally Implicit Runge-Kutta Methods with Error Estimators
Yousef Alamri, David I. Ketcheson
A numerical search approach is used to design high-order diagonally implicit Runge-Kutta (DIRK) schemes equipped with embedded error estimators, some of which have identical diagon…
A Comparative Study of Iterative Riemann Solvers for the Shallow Water and Euler Equations
Carlos Muñoz Moncayo, Manuel Quezada de Luna, David I. Ketcheson
The Riemann problem for first-order hyperbolic systems of partial differential equations is of fundamental importance for both theoretical and numerical purposes. Many approximate…
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…