Zobrazeno 1 - 10
of 17
pro vyhledávání: '"Lajos Lóczi"'
Publikováno v:
Numerische Mathematik. 146:875-906
Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge-Kutta methods. We generalize this approach to multistep methods, includ
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a527e345e165e6ed7da349661d51bf83
https://doi.org/10.1007/s00211-020-01158-4
https://doi.org/10.1007/s00211-020-01158-4
Publikováno v:
SIAM Journal on Numerical Analysis. 54:2799-2832
Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e70df56138088e898015e59cd1353fcc
https://doi.org/10.1137/15m101717x
https://doi.org/10.1137/15m101717x
Publikováno v:
J SCI COMPUT JOURNAL OF SCIENTIFIC COMPUTING.
We investigate dense output formulae (also known as continuous extensions) for strong stability preserving (SSP) Runge---Kutta methods. We require that the dense output formula also possess the SSP property, ideally under the same step-size restricti
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::45d971257d9f9baeac96f3f704e608da
http://hdl.handle.net/10831/48918
http://hdl.handle.net/10831/48918
Publikováno v:
SIAM Journal on Numerical Analysis. 52:2227-2249
In practical computation with Runge-Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so forth. We show by example that propagation of such errors within a single step can have catastro
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https://explore.openaire.eu/search/publication?articleId=doi_________::db1a7be28e184818a86d80468d4c88ec
https://doi.org/10.1137/130936245
https://doi.org/10.1137/130936245
We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a95770ec62dc8ed33e504cce87997d39
http://arxiv.org/abs/1610.00228
http://arxiv.org/abs/1610.00228
Autor:
Lajos Lóczi
Linear multistep methods (LMMs) applied to approximate the solution of initial value problems---typically arising from method-of-lines semidiscretizations of partial differential equations---are often required to have certain monotonicity or boundedn
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::aa038d2e9504f1841b9f7707d0990df4
Autor:
Lajos Lóczi, Joseph Páez Chávez
Publikováno v:
Differential Equations and Dynamical Systems. 20:235-284
In this article we present several results concerning the discretization of dynamical systems near bifurcation points. Special emphasis is put on codimension one and two cases as well as on the corresponding bifurcation diagrams. In some cases, we sh
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::30bc98c889cee8ceaf51fdf4c66eda7c
https://doi.org/10.1007/s12591-012-0135-5
https://doi.org/10.1007/s12591-012-0135-5
Autor:
Barnabas M. Garay, Lajos Lóczi
Publikováno v:
Periodica Mathematica Hungarica. 56:37-53
In the vicinity of fold bifurcation points, the time-h exact and the stepsize-h discretized dynamics are shown to be equivalent via a two-parameter family of conjugacies. The problem of optimal conjugacy estimates remains open.
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https://explore.openaire.eu/search/publication?articleId=doi_________::69eb58687e1986ebe162464e2fb2db8a
https://doi.org/10.1007/s10998-008-5037-1
https://doi.org/10.1007/s10998-008-5037-1
Autor:
Lajos Lóczi
We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions on the one-step discretiza
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f299a1b12a88fe56a0abaffab1339a80
http://arxiv.org/abs/1411.6252
http://arxiv.org/abs/1411.6252
Autor:
David I. Ketcheson, Lajos Lóczi
We study the radius of absolute monotonicity $R$ of rational functions with numerator and denominator of degree $s$ that approximate the exponential function to order $p$. Such functions arise in the application of implicit $s$-stage, order $p$ Runge
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fba82d8d636577a8eec1004af186190a
http://arxiv.org/abs/1303.6651
http://arxiv.org/abs/1303.6651