相关论文: Exponentially fitted methods that preserve conserv…

Because of the finiteness of the life span and boundedness of the physical space, the more reasonable or physical choice is the tempered power-law instead of pure power-law for the CTRW model in characterizing the waiting time and jump…

We have shown previously that functionally fitted Runge-Kutta (FRK) methods can be studied using a convenient collocation framework. Here, we extend that framework to functionally fitted Runge-Kutta-Nystr\"om (FRKN) methods, shedding…

This work presents a new evolutionary optimization algorithm in theoretical mathematics with important applications in scientific computing. The use of the evolutionary algorithm is justified by the difficulty of the study of the…

In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned averaged vector field method. This leads to numerical schemes…

In this paper, we present a comprehensive long-time stability analysis of a second-order explicit exponential Runge--Kutta (ERK2) method for the Cahn--Hilliard (CH) equation. By employing Fourier spectral collocation in space and a…

A class of linear kinetic Fokker-Planck equations with a non-trivial diffusion matrix and with periodic boundary conditions in the spatial variable is considered. After formulating the problem in a geometric setting, the question of the…

This paper investigates the energy conservation properties of explicit Runge--Kutta (RK) time discretizations for autonomous skew-symmetric systems. For linear problems, we present a general framework for constructing RK methods in which…

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…

Resummation methods using continued functions are implemented to converge divergent series appearing in perturbation problems related to continuous phase transitions in field theories. In some cases, better convergence properties are…

Modeling of kinetic plasmas using electromagnetic particle in cell methods (EM-PIC) is a problem that is well worn, in that methods developed have been used extensively both understanding physics and exploiting them for device design.…

A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta methods is devised. Intended for semidiscretizations of hyperbolic partial differential equations, the herein developed approach…

The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take…

Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were proposed and analyzed in 4. These specially designed methods use reduced precision for the implicit computations and full…

We introduce a high-order space-time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP) and well-balanced with respect to rest states. The employed time-stepping technique is a novel explicit…

In this paper, we present continuous-stage partitioned Runge-Kutta (csPRK) methods for energy-preserving integration of Hamiltonian systems. A sufficient condition for the energy preservation of the csPRK methods is derived. It is shown…

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 by multiple time stepping algorithms. Similar to the…

Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible…

Perturbed Runge--Kutta methods (also referred to as downwind Runge--Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge--Kutta counterparts. In this paper we study, the question…

Next-generation exascale machines with extreme levels of parallelism will provide massive computing resources for large scale numerical simulations of complex physical systems at unprecedented parameter ranges. However, novel numerical…

We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…