Zobrazeno 1 - 10
of 58
pro vyhledávání: '"LÓCZI, LAJOS"'
We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical experiments sugge
Externí odkaz:
http://arxiv.org/abs/2311.02603
Autor:
Fekete, Imre, Lóczi, Lajos
In this work, we further investigate the application of the well-known Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for numerically solving initial-value problems of
Externí odkaz:
http://arxiv.org/abs/2307.01345
Autor:
Fekete, Imre, Lóczi, Lajos
In this work, we study the application the classical Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for solving initial-value problems of systems of ordinary different
Externí odkaz:
http://arxiv.org/abs/2206.10220
We analyze, from the viewpoint of positivity preservation, certain discretizations of a fundamental partial differential equation, the one-dimensional advection equation with periodic boundary condition. The full discretization is obtained by couplin
Externí odkaz:
http://arxiv.org/abs/2105.07403
Autor:
Lóczi, Lajos
Solutions to a wide variety of transcendental equations can be expressed in terms of the Lambert $\mathrm{W}$ function. The $\mathrm{W}$ function, occurring frequently in applications, is a non-elementary, but now standard mathematical function imple
Externí odkaz:
http://arxiv.org/abs/2008.06122
Publikováno v:
Numerische Mathematik, 2020
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:
http://arxiv.org/abs/2003.03012
Autor:
Lóczi, Lajos
In this work we study the stability regions of linear multistep or multiderivative multistep methods for initial-value problems by using techniques that are straightforward to implement in modern computer algebra systems. In many applications, one is
Externí odkaz:
http://arxiv.org/abs/1901.08347
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
Externí odkaz:
http://arxiv.org/abs/1610.00228
Autor:
Lóczi, Lajos
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:
http://arxiv.org/abs/1609.07858