Results 221 to 230 of about 51,201 (262)

Group Velocity in Finite Difference Schemes

SIAM Review, 1982
The relevance of group velocity to the behavior of finite difference models of time-dependent partial differential equations is surveyed and illustrated. Applications involve the propagation of wave packets in one and two dimensions, numerical dispersion, the behavior of parasitic waves, and the stability analysis of initial boundary-value problems.
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AN INTRODUCTION TO NONSTANDARD FINITE DIFFERENCE SCHEMES

Journal of Computational Acoustics, 1999
Nonstandard finite difference schemes offer the potential for either constructing exact discrete models of differential equations or obtaining discrete models that do not have the elementary numerical instabilities. While the general laws for constructing such schemes are not precisely known at the present time, a number of important rules have been ...
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A finite difference scheme on nonuniform grids

International Journal of Computer Mathematics, 2001
In the present work, we introduce a finite difference scheme on an nonuniform grid. The truncation errors introduced by the use of this difference scheme is presented. It is shown that the numerical solution in the physical domain on nonuniform grids has some advantages.
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On Monotonic Finite Difference Schemes

Mathematical Models and Computer Simulations, 2020
We propose an approach to construct monotonic finite difference schemes for solving the simplest elliptic and parabolic equations with the first derivatives and a small parameter at the highest derivative. For this, the notion of adaptive artificial viscosity is introduced.
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A combined scheme of finite elements and finite differences

Journal of the Franklin Institute, 1989
Two-dimensional boundary value problems for the Laplace equation in a ring-like region are considered. The differential equation is written first in polar coordinates and then reformulated in terms of a dimensionless radial variable. An approximate solution is assumed as the sum of products of functions of the radial and the angular variables, for ...
Yano, H., Kieda, A., Nishioka, K.
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Exact finite difference and non-standard finite difference schemes for

Journal of Difference Equations and Applications, 2011
Exact finite difference schemes and non-standard finite difference schemes are constructed for the first-order differential equation , for and . In particular, we show that the central finite difference scheme is an exact scheme for the differential equation .
Lih-Ing Wu Roeger, Ronald E. Mickens
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Chaos in Finite Difference Schemes

2003
Publisher Summary The word “chaos” appeared for the first time in the field of mathematics in an article of Li and Yorke entitled “Period Three Implies Chaos.” This short and elegant paper caused a great sensation in the world of mathematical physics.
Masaya Yamaguti, Yoichi Maeda
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Finite-Difference Schemes on Regular Triangular Grids

Journal of Computational Physics, 1993
The authors consider wave propagation errors of linear convection equations in one and two spatial dimensions (1) \(U_ t + c \cdot \text{grad} U = 0\). For the analytical solution an ansatz of harmonic functions is made. This is compared with some numerical semidiscrete approximations of (1). In the 2D-case finite difference schemes are considered on a
Zingg, David W., Lomax, Harvard
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Asymptotic Behavior of Solutions in Finite Difference Schemes

Bulletin of the Russian Academy of Sciences: Physics, 2018
In many problems of numerically solving the Schrodinger equation, it is necessary to choose asymptotic distances that are many times greater than the characteristic size of the region of interaction. If the solutions to one-dimensional equations can be immediately chosen in a form that preserves unitarity, the preservation of probability (in, e.g., the
P. M. Krassovitskiy, F. M. Pen’kov
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Finite Difference Scheme for Barotropic Gas Equations

Doklady Mathematics, 2018
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Imranov, F. B., Kobel'kov, G. M., Sokolov, A. G.   +2 more
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