Explicit Nordsieck methods with quadratic stability

Authors:
Angelamaria Cardone;Zdzislaw Jackiewicz
Affiliations:
Dipartimento di Matematica, Università di Salerno, Fisciano (Sa), Italy 84084;Department of Mathematics, Arizona State University, Tempe, USA 85287 and AGH University of Science and Technology, Kraków, Poland
Venue:
Numerical Algorithms
Year:
2012

Citing 8
Cited 3

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Diagonally-implicit multi-stage integration methods

Applied Numerical Mathematics
A general class of two-step Runge-Kutta methods for ordinary differential equations

SIAM Journal on Numerical Analysis
Construction of high order diagonally implicit multistage integration methods for ordinary differential equations

Applied Numerical Mathematics
Construction of two-step Runge--Kutta methods with large regions of absolute stability

Journal of Computational and Applied Mathematics
Error propagation of general linear methods for ordinary differential equations

Journal of Complexity
Nordsieck representation of two-step Runge--Kutta methods for ordinary differential equations

Applied Numerical Mathematics
Two-step Runge-Kutta Methods with Quadratic Stability Functions

Journal of Scientific Computing

Search for efficient general linear methods for ordinary differential equations

Journal of Computational and Applied Mathematics
P-stable general Nyström methods for y˝=f(y(t))

Journal of Computational and Applied Mathematics
Extrapolation-based implicit-explicit general linear methods

Numerical Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

We describe the construction of explicit Nordsieck methods with s stages of order p驴=驴s驴驴驴1 and stage order q驴=驴p with inherent quadratic stability and quadratic stability with large regions of absolute stability. Stability regions of these methods compare favorably with stability regions of corresponding general linear methods of the same order with inherent Runge---Kutta stability.