1999
DOI: 10.1006/jcph.1999.6260
|View full text |Cite
|
Sign up to set email alerts
|

Optimal Runge–Kutta Methods for First Order Pseudospectral Operators

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

0
50
0
6

Year Published

2000
2000
2022
2022

Publication Types

Select...
7
1

Relationship

0
8

Authors

Journals

citations
Cited by 35 publications
(56 citation statements)
references
References 19 publications
0
50
0
6
Order By: Relevance
“…Concerning the latter, several options are at hand. Besides standard Runge-Kutta schemes of 3rd and 4th order, a numerically optimized 6-stage, 4th order Runge-Kutta scheme as proposed in [39] is available as well. A more detailed discussion can be found in [8].…”
Section: Eigenvalue and Initial Value Solvermentioning
confidence: 99%
“…Concerning the latter, several options are at hand. Besides standard Runge-Kutta schemes of 3rd and 4th order, a numerically optimized 6-stage, 4th order Runge-Kutta scheme as proposed in [39] is available as well. A more detailed discussion can be found in [8].…”
Section: Eigenvalue and Initial Value Solvermentioning
confidence: 99%
“…[39]. The corresponding coefficients are given in Table 1 and the stability boundaries are depicted in Fig.…”
Section: Stability Properties Of Relevant Explicit Runge-kutta Methodsmentioning
confidence: 99%
“…Section 4 highlights the salient features of some of our techniques of optimisation. In section 5, we use our techniques of optimisation to find optimal values of β 5 and β 6 and then perform a comparison of the spectral analysis of the dispersive and dissipative properties of the Runge Kutta schemes constructed by Hu et al [14], Mead and Renaut [19], Tselios and Simos [25] with our new Runge-Kutta scheme. In section 6, we present the results of a numerical experiment dealing with a convective wave equation and a non-linear spherical wave problem using four different schemes and compare some types of errors.…”
Section: Organisation Of Papermentioning
confidence: 99%
“…Stanescu and Habashi [21] propose a special Runge-Kutta scheme that can be written using minimum storage (i.e 2N-storage where N is the dimension of the first order differential system). Mead and Renaut [19] propose a six-stage fourth order Runge-Kutta method, in the context of Chebyshev pseudospectral discretization, with extended stability along the imaginary axis. Berland et al [9] have constructed an explicit low-storage fourth-order six-stage Runge-Kutta scheme optimized in the Fourier space with a large stability range.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation