相关论文: Higher-Order Energy-Decreasing Exponential Time Di…
In this paper we propose and analyze a (temporally) third order accurate exponential time differencing (ETD) numerical scheme for the no-slope-selection (NSS) equation of the epitaxial thin film growth model, with Fourier pseudo-spectral…
Explicit Runge-Kutta methods are classical and widespread techniques in the numerical solution of ordinary differential equations (ODEs). Considering partial differential equations, spatial semidiscretisations can be used to obtain systems…
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…
In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving…
In this paper, a class of arbitrarily high-order linear momentum-preserving and energy-preserving schemes are proposed, respectively, for solving the regularized long-wave equation. For the momentum-preserving scheme, the key idea is based…
We present a second-order strictly length-preserving and unconditionally energy-stable rotational discrete gradient (Rdg) scheme for the numerical approximation of the Oseen-Frank gradient flows with anisotropic elastic energy functional.…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
We provide a note on continuous-stage Runge-Kutta methods (csRK) for solving initial value problems of first-order ordinary differential equations. Such methods, as an interesting and creative extension of traditional Runge-Kutta (RK)…
Strong Stability Preserving (SSP) time integration schemes maintain stability of the forward Euler method for any initial value problem. However, only a small subset of Runge-Kutta (RK) methods are SSP, and many efficient high-order time…
A novel class of high-order linearly implicit energy-preserving integrating factor Runge-Kutta methods are proposed for the nonlinear Schr\"odinger equation. Based on the idea of the scalar auxiliary variable approach, the original equation…
Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high…
An efficient third-order discrete unified gas kinetic scheme (DUGKS) with efficiency is presented in this work for simulating continuum and rarefied flows. By employing two-stage time-stepping scheme and the high-order DUGKS flux…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…
This paper investigates the competitiveness of semi-implicit Runge-Kutta (RK) and spectral deferred correction (SDC) time-integration methods up to order six for incompressible Navier-Stokes problems in conjunction with a high-order…
In this work we present a class of high order unconditionally strong stability preserving (SSP) implicit multi-derivative Runge--Kutta schemes, and SSP implicit-explicit (IMEX) multi-derivative Runge--Kutta schemes where the time-step…
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 diagonal elements (SDIRK) and explicit first stage (ESDIRK). In…
In \cite{BDM2003} the modified Patankar-Euler and modified Patankar-Runge-Kutta schemes were introduced to solve positive and conservative systems of ordinary differential equations. These modifications of the forward Euler scheme and…
We develop an efficient, unconditionally stable, variable step second order exponential time differencing scheme for the incompressible Navier Stokes equations in two and three spatial dimensions under periodic boundary conditions, together…
In a previous paper, a technique was suggested to avoid order reduction with any explicit exponential Runge-Kutta method when integrating initial boundary value nonlinear problems with time-dependent boundary conditions. In this paper, we…
In this paper, we present a novel class of high-order Runge--Kutta (RK) discontinuous Galerkin (DG) schemes for hyperbolic conservation laws. The new method extends beyond the traditional method of lines framework and utilizes…