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1984
To arrive at finite difference equations modeling magnetohydrodynamic equilibrium we use a technique that is motivated by the finite element method [3]. First we develop a second order accurate numerical quadrature formula for the Hamiltonian E based on a rectangular grid of mesh points over a unit cube of the space with coordinates s, u and v.
Frances Bauer +2 more
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To arrive at finite difference equations modeling magnetohydrodynamic equilibrium we use a technique that is motivated by the finite element method [3]. First we develop a second order accurate numerical quadrature formula for the Hamiltonian E based on a rectangular grid of mesh points over a unit cube of the space with coordinates s, u and v.
Frances Bauer +2 more
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Group Velocity in Finite Difference Schemes
SIAM Review, 1982The 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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2020
Due to its relative simplicity, finite-difference (FD) analysis was historically the first numerical technique for boundary value problems in mathematical physics.
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Due to its relative simplicity, finite-difference (FD) analysis was historically the first numerical technique for boundary value problems in mathematical physics.
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AN INTRODUCTION TO NONSTANDARD FINITE DIFFERENCE SCHEMES
Journal of Computational Acoustics, 1999Nonstandard 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, 2001In 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, 2020We 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, 1989Two-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, 2011Exact 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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On a Finite-Difference Scheme for an Hereditary Oscillatory Equation
Journal of Mathematical Sciences, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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