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09/05/2023
Accurate Solution of the Nonlinear Schrödinger Equation via Conservative Multiple-Relaxation ImEx Methods
The nonlinear Schrödinger (NLS) equation possesses an infinite hierarchy...
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07/21/2023
A high-order finite volume method for Maxwell's equations in heterogeneous and time-varying media
We develop a finite volume method for Maxwell's equations in materials w...
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05/23/2023
Order conditions for Runge–Kutta-like methods with solution-dependent coefficients
In recent years, many positivity-preserving schemes for initial value pr...
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02/10/2023
Multiple-Relaxation Runge Kutta Methods for Conservative Dynamical Systems
We generalize the idea of relaxation time stepping methods in order to p...
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11/26/2022
Very High-Order A-stable Stiffly Accurate Diagonally Implicit Runge-Kutta Methods
A numerical search approach is used to design high-order diagonally impl...
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09/25/2022
A Comparative Study of Iterative Riemann Solvers for the Shallow Water and Euler Equations
The Riemann problem for first-order hyperbolic systems of partial differ...
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11/23/2021
Computing with B-series
We present BSeries.jl, a Julia package for the computation and manipulat...
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09/17/2021
Maximum principle preserving space and time flux limiting for Diagonally Implicit Runge-Kutta discretizations of scalar convection-diffusion equations
We provide a framework for high-order discretizations of nonlinear scala...
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05/16/2021
Positivity preservation of implicit discretizations of the advection equation
We analyze, from the viewpoint of positivity preservation, certain discr...
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04/14/2021
Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics
We develop error-control based time integration algorithms for compressi...
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03/17/2021
Numerical simulation and entropy dissipative cure of the carbuncle instability for the shallow water circular hydraulic jump
We investigate the numerical artifact known as a carbuncle, in the solut...
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02/15/2021
On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations
We study the numerical error in solitary wave solutions of nonlinear dis...
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09/21/2020
A conservative fully-discrete numerical method for the regularised shallow water wave equations
The paper proposes a new, conservative fully-discrete scheme for the num...
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09/02/2020
Bound-preserving convex limiting for high-order Runge-Kutta time discretizations of hyperbolic conservation laws
We introduce a general framework for enforcing local or global inequalit...
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06/26/2020
A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations
We develop general tools to construct fully-discrete, conservative numer...
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05/13/2020
Positivity-Preserving Adaptive Runge-Kutta Methods
Many important differential equations model quantities whose value must ...
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03/06/2020
General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes
Recently, an approach known as relaxation has been developed for preserv...
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01/14/2020
Relaxation Runge-Kutta Methods for Hamiltonian Problems
The recently-introduced relaxation approach for Runge-Kutta methods can ...
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09/29/2019