相关论文: Performance evaluation of mixed-precision Runge-Ku…

In this work we consider a mixed precision approach to accelerate the implemetation of multi-stage methods. We show that Runge-Kutta methods can be designed so that certain costly intermediate computations can be performed as a…

Mixed precision Runge--Kutta methods have been recently developed and used for the time-evolution of partial differential equations. Two-derivative Runge--Kutta schemes may offer enhanced stability and accuracy properties compared to…

Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were proposed and analyzed in [8]. These specially designed methods use reduced precision or the implicit computations and full…

Mixed-precision methods combine low and high precision arithmetics to exploit low precision computational speed and high precision accuracy. Large ODE systems that contain many heterogeneous interactions lead to a high computational cost…

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…

Mixed-precision algorithms combine low- and high-precision computations in order to benefit from the performance gains of reduced-precision without sacrificing accuracy. In this work, we design mixed-precision Runge-Kutta-Chebyshev (RKC)…

We consider the efficient numerical solution of coupled dynamical systems, consisting of a small nonlinear part and a large linear time invariant part, possibly stemming from spatial discretization of an underlying partial differential…

This paper discusses stochastic numerical methods of Runge-Kutta type with weak and strong convergences for systems of stochastic differential equations in It\^o form. At the beginning we give a brief overview of the stochastic numerical…

In this paper the performance of a parallel iterated Runge-Kutta method is compared versus those of the serial fouth order Runge-Kutta and Dormand-Prince methods. It was found that, typically, the runtime for the parallel method is…

A mixed accuracy framework for Runge--Kutta methods presented in Grant [JSC 2022] and applied to diagonally implicit Runge--Kutta (DIRK) methods can significantly speed up the computation by replacing the implicit solver by less expensive…

Dynamic systems have a fundamental relevance in the description of physical phenomena. The search for more accurate and faster numerical integration methods for the resolution of such systems is, therefore, an important topic of research.…

In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…

A methodology that can generate the optimal coefficients of a numerical method with the use of an artificial neural network is presented in this work. The network can be designed to produce a finite difference algorithm that solves a…

We study Runge-Kutta methods for rough differential equations which can be used to calculate solutions to stochastic differential equations driven by processes that are rougher than a Brownian motion. We use a Taylor series representation…

A focus of recent research in quantum computing has been on developing quantum algorithms for differential equations solving using variational methods on near-term quantum devices. A promising approach involves variational algorithms, which…

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…

This paper illuminates the derivation, the applicability, and the efficiency of the Multiplicative Runge-Kutta Method, derived in the frame- work of geometric multiplicative calculus. The removal of the restrictions of geometric…

A space-time fully adaptive multiresolution method for evolutionary non-linear partial differential equations is presented introducing an improved local time-stepping method. The space discretisation is based on classical finite volumes,…

Multiphysics systems are driven by multiple processes acting simultaneously, and their simulation leads to partitioned systems of differential equations. This paper studies the solution of partitioned systems of differential equations using…

Mixed-precision computing has the potential to significantly reduce the cost of exascale computations, but determining when and how to implement it in programs can be challenging. In this article, we propose a methodology for enabling…