Zobrazeno 1 - 10
of 234
pro vyhledávání: '"Ernst Hairer"'
Autor:
Walter Gautschi, Ernst Hairer
Publikováno v:
Journal of Inequalities and Applications, Vol 2019, Iss 1, Pp 1-27 (2019)
Abstract The conjectures in the title deal with the zeros xj $x_{j}$, j=1,2,…,n $j=1,2, \ldots ,n$, of an orthogonal polynomial of degree n>1 $n>1$ relative to a nonnegative weight function w on an interval [a,b] $[a,b]$ and with the respective ele
Externí odkaz:
https://doaj.org/article/4b3acb6a7e7b4b8783066a7691e15ad5
The first book to approach high oscillation as a subject of its own, Highly Oscillatory Problems begins a new dialogue and lays the groundwork for future research. It ensues from the six-month programme held at the Newton Institute of Mathematical Sc
Autor:
Nicola Guglielmi, Ernst Hairer
Publikováno v:
Numerical Algorithms.
We consider piecewise-smooth dynamical systems, i.e., systems of ordinary differential equations switching between different sets of equations on distinct domains, separated by hyper-surfaces. As is well-known, when the solution approaches a disconti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::016082479b6b45389ac82e6567f2c209
https://doi.org/10.1007/s11075-023-01499-9
https://doi.org/10.1007/s11075-023-01499-9
Publikováno v:
BIT Numerical Mathematics. 61:805-827
The study of convergence of time integrators, applied to linear discretized PDEs, relies on the power boundedness of the stability matrix R. The present work investigates power boundedness in the maximum norm for ADI-type integrators in arbitrary spa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7596f8d5c79d86272ac65c5dfe7e5d59
https://doi.org/10.1007/s10543-021-00845-4
https://doi.org/10.1007/s10543-021-00845-4
Autor:
Christian Lubich, Ernst Hairer
Publikováno v:
Numerische Mathematik. 144:699-728
The differential equations of motion of a charged particle in a strong non-uniform magnetic field have the magnetic moment as an adiabatic invariant. This quantity is nearly conserved over long time scales covering arbitrary negative powers of the sm
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6904c589d5c3eba25d143532200e3b6e
https://doi.org/10.1007/s00211-019-01093-z
https://doi.org/10.1007/s00211-019-01093-z
Publikováno v:
SIAM Journal on Numerical Analysis. 58:1117-1137
For the numerical solution of parabolic problems with a linear diffusion term, linearly implicit time integrators are considered. To reduce the cost on the linear algebra level, an alternating dire...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b79cc8ea8a8586b3a8d44f069c771c38
https://doi.org/10.1137/19m1246262
https://doi.org/10.1137/19m1246262
Autor:
Ernst Hairer, Nicola Guglielmi
Publikováno v:
Numerical algorithms. 89(3)
This article considers the numerical treatment of piecewise-smooth dynamical systems. Classical solutions as well as sliding modes up to codimension-2 are treated. An algorithm is presented that, in the case of non-uniqueness, selects a solution that
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5cf063b89273f847964595de463deffc
https://pubmed.ncbi.nlm.nih.gov/35185303
https://pubmed.ncbi.nlm.nih.gov/35185303
Autor:
Ernst Hairer, Christian Lubich
Publikováno v:
BIT Numerical Mathematics. 58:969-979
The Boris algorithm is a widely used numerical integrator for the motion of particles in a magnetic field. This article proves near-conservation of energy over very long times in the special cases where the magnetic field is constant or the electric
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a90b3776d18d2e2cda0df73721db418a
https://doi.org/10.1007/s10543-018-0713-1
https://doi.org/10.1007/s10543-018-0713-1
Autor:
Ernst Hairer, Christian Lubich
Publikováno v:
The SMAI journal of computational mathematics. 3:205-218
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::91914ea612a5dd99074de622d2cf6121
https://doi.org/10.5802/smai-jcm.25
https://doi.org/10.5802/smai-jcm.25
Publikováno v:
Numerical Algorithms. 78:957-981
The present work considers the numerical solution of differential equations that are obtained by space discretization (method of lines) of parabolic evolution equations. Main emphasis is put on the presence of mixed derivatives in the elliptic operat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::12971ee1239801d29e41378bf22e50a7
https://doi.org/10.1007/s11075-017-0408-8
https://doi.org/10.1007/s11075-017-0408-8