Finite difference coefficient

About: Finite difference coefficient is a research topic. Over the lifetime, 3075 publications have been published within this topic receiving 57485 citations.

A novel finite difference formulation for differential expressions involving both first and second derivatives

Abstract: It is shown that the upwind difference scheme of formulating differential expressions, in problems involving transport by simultaneous convection and diffusion, is superior to the central differences scheme, when the local Peclet number of the grid is large. Even better schemes are derived and discussed. It is pointed out that the best finite differences analogues are found by approximating differential expressions as a whole, and that simple (e.g. one-dimensional) exact solutions form a useful, legitimate and independent source of these optimum algebraic formulae.

Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures*

Abstract: Finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form $cu_t + bu_x - (au_x )_x = f$. Optimal order error estimates in $L^2 $ and $W^{1,2} $ are derived for the finite element procedure. Various error estimates are presented for a variety of finite difference methods. The estimates show that, for convection-dominated problems $(b \gg a)$, these schemes have much smaller time-truncation errors than those of standard methods. Extensions to n-space variables and time-dependent or nonlinear coefficients are indicated, along with applications of the concepts to certain problems described by systems of differential equations.

Difference Equations and Inequalities: Theory, Methods, and Applications

Abstract: Preliminaries linear initial value problems miscellaneous difference equations difference inequalities qualitative properties of solutions of difference systems qualitative properties of solutions of higher order difference equations qualitative properties of solutions of neutral difference equations boundary value problems for linear systems boundary value problems for nonlinear systems miscellaneous properties of solutions of higher order linear difference equations boundary value problems for higher order difference equations Sturm-Liouville problems and related inequalities difference inequalities in several independent variables.

Generation of finite difference formulas on arbitrarily spaced grids

Abstract: On etablit des recurrences simples pour le calcul des poids dans les formules aux differences finies compactes pour les derivees de tous ordres avec une precision d'ordre arbitraire sur des grilles a une dimension d'espacement arbitraire