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pro vyhledávání: '"DITKOWSKI, ADI"'
Finite Difference methods (FD) are one of the oldest and simplest methods for solving partial differential equations (PDE). Block Finite Difference methods (BFD) are FD methods in which the domain is divided into blocks, or cells, containing two or m
Externí odkaz:
http://arxiv.org/abs/2407.03338
We propose a block finite difference, error inhibiting scheme that is fourth-order accurate for short to moderate times and has a six-order convergence rate for long times. This scheme outperforms the standard fourth-order Finite Difference scheme. W
Externí odkaz:
http://arxiv.org/abs/2402.11617
Finite Difference methods (FD) are one of the oldest and simplest methods for solving partial differential equations (PDE). Block Finite Difference methods (BFD) are FD methods in which the domain is divided into blocks, or cells, containing two or m
Externí odkaz:
http://arxiv.org/abs/2011.14411
Autor:
Ditkowski, Adi, Shustin, Paz Fink
Finite Difference (FD) schemes are widely used in science and engineering for approximating solutions of partial differential equations (PDEs). Error analysis of FD schemes relies on estimating the truncation error at each time step. This approach us
Externí odkaz:
http://arxiv.org/abs/2010.00476
High order implicit-explicit (IMEX) methods are often desired when evolving the solution of an ordinary differential equation that has a stiff part that is linear and a non-stiff part that is nonlinear. This situation often arises in semi-discretizat
Externí odkaz:
http://arxiv.org/abs/1912.10027
High order methods are often desired for the evolution of ordinary differential equations, in particular those arising from the semi-discretization of partial differential equations. In prior work in we investigated the interplay between the local tr
Externí odkaz:
http://arxiv.org/abs/1912.04159
Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods, and more broadly general linear methods, all have a global error that
Externí odkaz:
http://arxiv.org/abs/1910.02937
A dynamical system is said to be reversible if, given an output, the input can always be recovered in a well-posed manner. Nevertheless, we argue that reversible systems that have a time-reversal symmetry, such as the Nonlinear Schr{\"o}dinger equati
Externí odkaz:
http://arxiv.org/abs/1905.11291
Autor:
Patwardhan, Gauri, Gao, Xiaohui, Sagiv, Amir, Dutt, Avik, Ginsberg, Jared, Ditkowski, Adi, Fibich, Gadi, Gaeta, Alexander
Publikováno v:
Phys. Rev. A 99, 033824 (2019)
We show theoretically and demonstrate experimentally that collapsing elliptically-polarized laser beams experience a nonlinear ellipse rotation that is highly sensitive to small fluctuations in the input power. For arbitrarily small fluctuations in t
Externí odkaz:
http://arxiv.org/abs/1808.07019
The effect of uncertainties and noise on a quantity of interest (model output) is often better described by its probability density function (PDF) than by its moments. Although density estimation is a common task, the adequacy of approximation method
Externí odkaz:
http://arxiv.org/abs/1803.10991