The potential for parallelism in Runge–Kutta methods. Part 1: RK formulas in standard form

KR Jackson, SP Nørsett - SIAM journal on numerical analysis, 1995 - SIAM
The authors examine the potential for parallelism in Runge–Kutta (RK) methods based on
formulas in standard one-step form. Both negative and positive results are presented. Many …

B–series analysis of stochastic Runge–Kutta methods that use an iterative scheme to compute their internal stage values

K Debrabant, A Kværnø - SIAM journal on numerical analysis, 2009 - SIAM
In recent years, implicit stochastic Runge–Kutta (SRK) methods have been developed both
for strong and weak approximations. For these methods, the stage values are only given …

Envelope-following method to compute steady-state solutions of electrical circuits

A Brambilla, P Maffezzoni - IEEE Transactions on Circuits and …, 2003 - ieeexplore.ieee.org
The paper deals with the determination of the steady-state solution of both autonomous and
nonautonomous circuits. Only time-domain methods are considered, and, in particular, the …

Parallelizing spectral deferred corrections across the method

R Speck - Computing and visualization in science, 2018 - Springer
In this paper we present two strategies to enable “parallelization across the method” for
spectral deferred corrections (SDC). Using standard low-order time-stepping methods in an …

PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method

R Schöbel, R Speck - Computing and visualization in science, 2020 - Springer
To extend prevailing scaling limits when solving time-dependent partial differential
equations, the parallel full approximation scheme in space and time (PFASST) has been …

Runge-kutta research at toronto

TE Hull, WH Enright, KR Jackson - Applied numerical mathematics, 1996 - Elsevier
The main purpose of this paper is to review the work on Runge-Kutta methods at the
University of Toronto during the period 1963 to the present (1996). To provide some …

[PDF][PDF] Review Paper on the Runge-Kutta Methods to Study Numerical Solutions of Initial Value Problems in Ordinary Differential Equations

PL Sharma, A Kumar - … Journal of Applied Mathematics and Statistical …, 2021 - academia.edu
The main purpose of this article is to review the work on Runge-Kutta Methods to study on
Numerical Solutions of Initial Value Problems in Ordinary Differential Equations during the …

[HTML][HTML] IRK methods for DAE: Starting algorithms

T Roldán, I Higueras - Journal of computational and applied mathematics, 1999 - Elsevier
When semi-explicit differential-algebraic equations are solved with implicit Runge–Kutta
methods, the computational effort is dominated by the cost of solving the nonlinear systems …

An analysis of the order of Runge-Kutta methods that use an iterative scheme to compute their internal stage values

KR Jackson, A Kværnø, SP Nørsett - BIT Numerical Mathematics, 1996 - Springer
We employ B-series to analyze the order of Runge-Kutta (RK) methods that use simple
iteration, modified Newton iteration or full Newton iteration to compute their internal stage …

Construction of starting algorithms for the RK-Gauss methods

MP Laburta - Journal of computational and applied mathematics, 1998 - Elsevier
In this paper starting algorithms for the numerical solution of stage equations in Runge-Kutta-
Gauss formulae with 2, 3 and 4 stages are constructed. For each of these formulae, three …