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The numerical simulation of three-dimensional charged-particle dynamics (CPD) under strong magnetic field is a basic and challenging algorithmic task in plasma physics. In this paper, we introduce a new methodology to design two-scale exponential int
Externí odkaz:
http://arxiv.org/abs/2311.18615
Autor:
Carrel, Benjamin, Vandereycken, Bart
The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and have been
Externí odkaz:
http://arxiv.org/abs/2312.00172
In this paper, we introduce a novel numerical approach for approximating the SIR model in epidemiology. Our method enhances the existing linearization procedure by incorporating a suitable relaxation term to tackle the transcendental equation of nonl
Externí odkaz:
http://arxiv.org/abs/2308.08106
Publikováno v:
IMA Journal of Numerical Analysis, 2024
We introduce and analyze an $hp$-version $C^1$-continuous Petrov-Galerkin (CPG) method for nonlinear initial value problems of second-order ordinary differential equations. We derive a-priori error estimates in the $L^2$-, $L^\infty$-, $H^1$- and $H^
Externí odkaz:
http://arxiv.org/abs/2303.14345
Autor:
Wang, Bin, Jiang, Yaolin
The aim of this paper is to formulate and analyze numerical discretizations of charged-particle dynamics (CPD) in a strong nonuniform magnetic field. A strategy is firstly performed for the two dimensional CPD to construct the semi-discretization and
Externí odkaz:
http://arxiv.org/abs/2205.08191
Publikováno v:
Appl. Numer. Math. 146 (2019), 400-415
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the additional
Externí odkaz:
http://arxiv.org/abs/1903.05391
We deal with the approximate solution of initial value problems in infinite-dimensional Banach spaces with a Schauder basis. We only allow finite-dimensional algorithms acting in the spaces $\rr^N$, with varying $N$. The error of such algorithms depe
Externí odkaz:
http://arxiv.org/abs/1712.06514
Autor:
Kacewicz, Boleslaw
Publikováno v:
J. Complexity, 47, 86-96, 2018
It is known that, for systems of initial-value problems, algorithms using adaptive information perform much better in the worst case setting than the algorithms using nonadaptive information. In the latter case, lower and upper complexity bounds sign
Externí odkaz:
http://arxiv.org/abs/1709.09951
Publikováno v:
Proceedings of the 17th International Conference on Computational and Mathematical Methods in Science and Engineering CMMSE-2017, (2017) 1198-1206
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that they are obt
Externí odkaz:
http://arxiv.org/abs/1708.00505
Autor:
Pulch, Roland
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity of intere
Externí odkaz:
http://arxiv.org/abs/1704.02284