相关论文: Strong Stability Preserving Integrating Factor Run…

A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP) in the sense that the time-dependent solution preserves for any time a uniform pointwise bound imposed by its initial and boundary conditions.…

A mixed accuracy framework for Runge--Kutta methods presented in [Grant, JSC 2022] has been shown to speed up the computation in diagonally implicit Runge--Kutta (DIRK) methods by using less expensive low accuracy approaches for the…

In this paper, we construct explicit nonstandard Runge-Kutta (ENRK) methods which have higher accuracy order and preserve two important properties of autonomous dynamical systems, namely, the positivity and linear stability. These methods…

We introduce a family of stochastic optimization methods based on the Runge-Kutta-Chebyshev (RKC) schemes. The RKC methods are explicit methods originally designed for solving stiff ordinary differential equations by ensuring that their…

The class of stochastic Runge-Kutta methods for stochastic differential equations due to R\"o{\ss}ler is considered. Coefficient families of diagonally drift-implicit stochastic Runge-Kutta (DDISRK) methods of weak order one and two are…

We propose an experimental study of adaptive time-stepping methods for efficient modeling of the aggregation-fragmentation kinetics. Precise modeling of this phenomena usually requires utilization of the large systems of nonlinear ordinary…

A unified theoretical framework is suggested to examine the energy dissipation properties at all stages of additive implicit-explicit Runge-Kutta (IERK) methods up to fourth-order accuracy for gradient flow problems. We construct some…

In this work, we develop a class of up to third-order energy-stable schemes for the Cahn--Hilliard equation. Building on Lawson's integrating factor Runge--Kutta method, which is widely used for stiff semilinear equations, we discuss its…

In this paper we present and analyze a general framework for constructing high order explicit local time stepping (LTS) methods for hyperbolic conservation laws. In particular, we consider the model problem discretized by Runge-Kutta…

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…

In this work modified Patankar-Runge-Kutta (MPRK) schemes up to order four are considered and equipped with a dense output formula of appropriate accuracy. Since these time integrators are conservative and positivity preserving for any time…

This paper is devoted to examining the stability of Runge-Kutta methods for solving nonlinear Volterra delay-integro-differential-algebraic equations (DIDAEs) with constant delay. Hybrid numerical schemes combining Runge-Kutta methods and…

Traditional time discretization methods use a single timestep for the entire system of interest and can perform poorly when the dynamics of the system exhibits a wide range of time scales. Multirate infinitesimal step (MIS) methods (Knoth…

We note a fact that stiff systems or differential equations that have highly oscillatory solutions cannot be solved efficiently using conventional methods. In this paper, we study two new classes of exponential Runge-Kutta (ERK) integrators…

The application of Runge-Kutta schemes designed to enjoy a large region of absolute stability can significantly increase the efficiency of numerical methods for PDEs based on a method of lines approach. In this work we investigate the…

We propose entropy-preserving and entropy-stable partitioned Runge--Kutta (RK) methods. In particular, we extend the explicit relaxation Runge--Kutta methods to IMEX--RK methods and a class of explicit second-order multirate methods for…

Many HPC applications that solve differential equations rely on the Runge-Kutta family of methods for time integration. Among these methods, the fourth-order accurate RK4 scheme is especially popular. This time integration scheme requires…

Segregated Runge-Kutta (SRK) schemes are time integration methods for the incompressible Navier-Stokes equations. In this approach, convection and diffusion can be independently treated either explicitly or implicitly, which in particular…

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 Hamiltonian systems) up to a given order in the step size,…

As supercomputers grow in hardware complexity, their susceptibility to faults increases and measures need to be taken to ensure the correctness of results. Some numerical algorithms have certain characteristics that allow them to recover…