Related papers: Performance Evaluation of Mixed-Precision Runge-Ku…
When applied to stiff, linear differential equations with time-dependent forcing, Runge-Kutta methods can exhibit convergence rates lower than predicted by the classical order condition theory. Commonly, this order reduction phenomenon is…
We propose a new probabilistic scheme which combines deep learning techniques with high order schemes for backward stochastic differential equations belonging to the class of Runge-Kutta methods to solve high-dimensional semi-linear…
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…
Explicit integrating factor Runge-Kutta methods are attractive and popular in developing high-order maximum bound principle preserving time-stepping schemes for Allen-Cahn type gradient flows. However, they always suffer from the…
Graph analytics techniques based on spectral methods process extremely large sparse matrices with millions or even billions of non-zero values. Behind these algorithms lies the Top-K sparse eigenproblem, the computation of the largest…
In this master thesis we have compared different second order stabilized explicit Runge-Kutta methods when applied to the incompressible Navier-Stokes equations by means of a projection method and a differential algebraic approach. We…
Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treat multiscale equations that contain a stiff part and a non-stiff part, where the stiff part is characterized by a small parameter $\varepsilon$. In this work, we…
This work constructs a new class of multirate schemes based on the recently developed generalized additive Runge-Kutta (GARK) methods (Sandu and Guenther, 2013). Multirate schemes use different step sizes for different components and for…
This work deals with two groups of spectral analysis results for matrices arising in fully implicit Runge-Kutta methods used for linear time-dependent partial differential equations. These were applied for different formulations of the same…
In this paper we derive and analyze the properties of explicit singly diagonal implicit Runge-Kutta (ESDIRK) integration methods. We discuss the principles for construction of Runge-Kutta methods with embedded methods of different order for…
We propose a unified theoretical framework to examine the energy dissipation properties at all stages of explicit exponential Runge-Kutta (EERK) methods for gradient flow problems. The main part of the novel framework is to construct the…
We propose an efficient algorithm for the approximation of fractional integrals by using Runge--Kutta based convolution quadrature. The algorithm is based on a novel integral representation of the convolution weights and a special…
The use of high order fully implicit Runge-Kutta methods is of significant importance in the context of the numerical solution of transient partial differential equations, in particular when solving large scale problems due to fine space…
In this work we present a new class of Runge-Kutta (RK) methods for solving systems of hyperbolic equations with a particular structure, generalization of a wave-equation. The new methods are {\it partially implicit} in the sense that a…
Variational space-time formulations for Partial Differential Equations have been of great interest in the last decades. While it is known that implicit time marching schemes have variational structure, the Galerkin formulation of explicit…
In this article, a family of two- and three-stage explicit multiquadric (MQ) and inverse multiquadric (IMQ) radial basis functions (RBFs) Runge-Kutta methods are introduced for solving ordinary differential equations. These methods are…
It is difficult to design high order numerical schemes which could preserve both the maximum bound property (MBP) and energy dissipation law for certain phase field equations. Strong stability preserving (SSP) Runge-Kutta methods have been…
In this paper, we develop a higher order symmetric partitioned Runge-Kutta method for a coupled system of differential equations on Lie groups. We start with a discussion on partitioned Runge-Kutta methods on Lie groups of arbitrary order.…
Fully implicit Runge-Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the…
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…