Related papers: High-order linearly implicit schemes conserving qu…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
We consider a Lattice Boltzmann type discrete velocity model in the low Mach number scaling and develop a corresponding numerical scheme that remains uniformly valid across all regimes of the mean free path, from the kinetic to the…
Parameterization (closure) schemes in numerical weather and climate prediction models account for the effects of physical processes that cannot be resolved explicitly by these models. Methods for finding physical parameterization schemes…
In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods are developed for the nonlinear Schr\"odinger equation by combining the scalar auxiliary variable approach with the exponential…
This work discusses the model reduction problem for large-scale multi-symplectic PDEs with cubic invariants. For this, we present a linearly implicit global energy-preserving method to construct reduced-order models. This allows to…
In this paper, we develop a novel, linearly implicit and local energy-preserving scheme for the sine-Gordon equation. The basic idea is from the invariant energy quadratization approach to construct energy stable schemes for gradient…
In this paper, we propose a class of explicit positivity preserving numerical methods for general stochastic differential equations which have positive solutions. Namely, all the numerical solutions are positive. Under some reasonable…
This paper concerns the numerical study for the generalized Rosenau-Kawahara-RLW equation obtained by coupling the generalized Rosenau-RLW equation and the generalized Rosenau-Kawahara equation. We first derive the energy conservation law…
We develop continuous-stage Runge-Kutta methods based on weighted orthogonal polynomials in this paper. There are two main highlighted merits for developing such methods: Firstly, we do not need to study the tedious solution of…
Non-local systems of conservation laws play a crucial role in modeling flow mechanisms across various scenarios. The well-posedness of such problems is typically established by demonstrating the convergence of robust first-order schemes.…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
This work considers multirate generalized-structure additively partitioned Runge-Kutta (MrGARK) methods for solving stiff systems of ordinary differential equations (ODEs) with multiple time scales. These methods treat different partitions…
Gradient flows of unit vector fields arise in a wide range of physical models such as harmonic map heat flows, nematic liquid crystals, and magnetization dynamics. Designing numerical schemes that simultaneously preserve the unit length…
In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are…
Motivated by studies on fully discrete numerical schemes for linear hyperbolic conservation laws, we present a framework on analyzing the strong stability of explicit Runge-Kutta (RK) time discretizations for semi-negative autonomous linear…
Higher-order time integration methods that unconditionally preserve the positivity and linear invariants of the underlying differential equation system cannot belong to the class of general linear methods. This poses a major challenge for…
We propose a new method that extends conservative explicit multirate methods to implicit explicit-multirate methods. We develop extensions of order one and two with different stability properties on the implicit side. The method is suitable…
Space discretization of some time-dependent partial differential equations gives rise to systems of ordinary differential equations in additive form whose terms have different stiffness properties. In these cases, implicit methods should be…
When one wishes to numerically solve an initial value problem, it is customary to rewrite it as an equivalent first-order system to which a method, usually from the class of Runge-Kutta methods, is applied. Directly treating higher-order…
We present a novel implicit scheme for the numerical solution of time-dependent conservation laws. The core idea of the presented method is to exploit and approximate the mixed spatial-temporal derivative of the solution that occurs…