zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A new type of singly-implicit Runge-Kutta method. (English) Zbl 0954.65058
The authors discuss new type of implicit Runge-Kutta methods which combine the singly-implicitness or diagonal-implicitness property with a zero first row in the coefficient matrix of the method. The new feature considered in this paper is the use of a first stage identical to the input approximation (this means that the first row of the coefficient matrix is zero) and the last stage , identical to the output value (this means that the last row of the coefficient matrix is identical with the vector of output value coefficients). The derived methods preserve the feature of the FSAL-methods and also of the DESI-methods [cf. {\it J. C. Butcher} and {\it J. R. Cash}, SIAM J. Numer. Anal. 27, No. 3, 753-761 (1990; Zbl 0702.65072)]. It is shown that the derivative of the first internal stage for a singly-implicit Runge-Kutta method can be obtained from the previous step without any loss of performance. Numerical experiments show the efficiency of the proposed methods.

65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
65L20Stability and convergence of numerical methods for ODE
Full Text: DOI