Zobrazeno 1 - 10
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pro vyhledávání: '"John C. Butcher"'
Autor:
John C. Butcher
Publikováno v:
Axioms, Vol 11, Iss 5, p 184 (2022)
A positive integer, which can be written as the sum of two positive cubes in two different ways, is known as a “Ramanujan number”. The most famous example is 1729=103+93=123+13, which was identified by Ramanujan as the lowest such number. In this
Externí odkaz:
https://doaj.org/article/9c7971d2022d4722a531cc10a4479b2f
Autor:
John C. Butcher
Publikováno v:
Axioms, Vol 7, Iss 3, p 52 (2018)
The traditional derivation of Runge–Kutta methods is based on the use of the scalar test problem y′(x)=f(x,y(x)). However, above order 4, this gives less restrictive order conditions than those obtained from a vector test problem using a tree-bas
Externí odkaz:
https://doaj.org/article/85da7247a3784b75b4127c4baaea7bde
Publikováno v:
Applied Numerical Mathematics. 187:71-88
In this paper, we propose linearly implicit and arbitrary high-order conservative numerical schemes for ordinary differential equations with a quadratic invariant. Many differential equations have invariants, and numerical schemes for preserving them
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c49e836c10e93dad631aa4870b24cf3
https://doi.org/10.1016/j.apnum.2023.02.005
https://doi.org/10.1016/j.apnum.2023.02.005
Autor:
John C. Butcher, Helmut Podhaisky
Publikováno v:
Journal of Computational and Applied Mathematics. 415:114480
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8033ab0b24314ca87e9d000ce5f165a3
https://doi.org/10.1016/j.cam.2022.114480
https://doi.org/10.1016/j.cam.2022.114480
Publikováno v:
Numerical Algorithms. 81:1403-1421
This paper describes the implementation of a class of IRKS methods (Wright 2002). These GLM algorithms are practical with reliable error estimators (Butcher and Podhaisky, Appl. Numer. Math. 56, 345–357 2006). The current robust ODE solvers in vari
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::97c2cc7f48ccdd88bdea8eebed5bd837
https://doi.org/10.1007/s11075-019-00663-4
https://doi.org/10.1007/s11075-019-00663-4
Autor:
John C. Butcher
Publikováno v:
B-Series ISBN: 9783030709556
One of the key questions in the analysis of numerical approximations to differential equations, and related problems, is in the comparison of two mappings. One mapping would be the exact flow through a specified time step and the other would be a num
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c6c2add1203cf7ae58e550fd607f88e0
https://doi.org/10.1007/978-3-030-70956-3_3
https://doi.org/10.1007/978-3-030-70956-3_3
Autor:
John C. Butcher
Publikováno v:
B-Series ISBN: 9783030709556
Integration methods were introduced as a generalization of Runge–Kutta methods in which the index set, usually a set of natural numbers, is replaced by a more complicated alternative, such as a closed interval. Equivalence and reducibility of metho
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::34e028f2fe98e093ee63f031bdfd82e0
https://doi.org/10.1007/978-3-030-70956-3_4
https://doi.org/10.1007/978-3-030-70956-3_4
Autor:
John C. Butcher
Publikováno v:
B-Series ISBN: 9783030709556
This book is concerned with the algebraic analysis of numerical methods and a good background in both ordinary differential equations and numerical methods for their solution is essential. In this chapter a very basic survey of these important topics
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3fd3769e91c7061d7f2b0d8592763a20
https://doi.org/10.1007/978-3-030-70956-3_1
https://doi.org/10.1007/978-3-030-70956-3_1
Autor:
John C. Butcher
Publikováno v:
B-Series ISBN: 9783030709556
The basic terminology of graphs, as vertex-edge pairs is presented, leading to the definitions of trees, in the sense of rooted trees, and unrooted, or free, trees. It is shown how to build up trees from the tree with a single vertex, using the beta-
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::11b0ae74d10053d2e01d5f385b340277
https://doi.org/10.1007/978-3-030-70956-3_2
https://doi.org/10.1007/978-3-030-70956-3_2
Autor:
John C. Butcher
Publikováno v:
B-Series ISBN: 9783030709556
Although it has not been possible to survey all aspects of the burgeoning subject of Geometric Integration, symplectic Runge–Kutta methods and their generalization to general linear methods are introduced to the extent that their main properties ar
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::54990430cb68eb2a889adb5747ca3ece
https://doi.org/10.1007/978-3-030-70956-3_7
https://doi.org/10.1007/978-3-030-70956-3_7