Zobrazeno 1 - 10
of 29
pro vyhledávání: '"J. H. Verner"'
Publikováno v:
Journal of Computational and Applied Mathematics. 290:44-64
We describe the derivation of order conditions, without restrictions on stage order, for general linear methods for ordinary differential equations. This derivation is based on the extension of the Albrecht approach proposed in the context of Runge-K
Autor:
J. H. Verner
Publikováno v:
Numerical Algorithms. 65:555-577
Explicit Runge–Kutta pairs of methods of successive orders of accuracy provide effective algorithms for approximating solutions to nonstiff initial value problems. For each explicit RK method of order of accuracy p, there is a minimum number s p of
Autor:
J. H. Verner, Anne Kværnø
Publikováno v:
Numerical Algorithms. 59:487-504
The representation of order conditions for general linear methods formulated using an algebraic theory by Butcher, and the alternative using B-series by Hairer and Wanner for treating vector initial value problems in ordinary differential equations a
Autor:
J. H. Verner
Publikováno v:
Numerical Algorithms. 53:383-396
Explicit Runge–Kutta pairs are known to provide efficient solutions to initial value differential equations with inexpensive derivative evaluations. Two criteria for selection are proposed with a view to deriving pairs of all orders 6(5) to 9(8) wh
Autor:
J. H. Verner
Publikováno v:
Applied Numerical Mathematics. 56:388-396
In [Japan JIAM 19 (2002) 227], Jackiewicz and Verner derived formulas for, and tested the implementation of two-step Runge-Kutta (TSRK) pairs. For pairs of orders 3 and 4, the error estimator accurately tracked the exact local truncation error on sev
Autor:
J. H. Verner
Publikováno v:
Journal of Computational and Applied Mathematics. 185(2):292-307
Jackiewicz and Tracogna [SIAM J. Numer. Anal. 32 (1995) 1390–1427] proposed a general formulation of two step Runge–Kutta (TSRK) methods. Using formulas for two-step pairs of TSRK methods constructed in [Japan JIAM 19 (2002) 227–248], Jackiewic
Autor:
J. H. Verner, Thomas A. Macdougall
Publikováno v:
Numerical Algorithms. 31:215-231
Dormand, Prince and their colleagues [3–5] showed in a sequence of papers that the approximation of an initial value differential system propagated by a Runge–Kutta pair, together with a continuous approximation obtained using additional derivati
Autor:
J. H. Verner, P. W. Sharp
Publikováno v:
Applied Numerical Mathematics. 34:261-274
The derivation of extended explicit Bel'tyukov pairs of methods for Volterra integral equations of the second kind is related to that of explicit Runge–Kutta pairs, but is more intricate. Techniques previously developed for deriving families of exp
Publikováno v:
Linear Algebra and its Applications. 312:191-195
A family of n×n symmetric circulant (0, 1) matrices is studied. It is shown that the determinant of each matrix is (−1) n−1 (n−1) , a property shared with the adjacency matrix of the complete graph on n nodes. As a result, each matrix in this
Autor:
J. H. Verner, P. W. Sharp
Publikováno v:
SIAM Journal on Numerical Analysis. 38:347-359
We derive and investigate a family of pairs of extended explicit Bel'tyukov Runge--Kutta (EBVRK) formulas to treat Volterra integral equations of the second kind. Each pair uses six stages and consists of an order 3 formula completely embedded in an