𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A frequency accurate spatial derivative finite difference approximation

✍ Scribed by Peter A. Orlin; A. Louise Perkins; George Heburn

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
163 KB
Volume
13
Category
Article
ISSN
0749-159X

No coin nor oath required. For personal study only.

✦ Synopsis

We present a method for designing spatial derivative approximations that achieves a priori accuracy in the spatial frequency domain. We use a general, average value approximation with undetermined coefficients together with a set of constraints that ensure convergence and consistency to formulate a constrained optimal fitting problem. These constraints lead to a linear matrix formulation. We apply the method to the design of spatial approximations for simulating equations with wavelike solutions using both an explicit central difference approximation (which has no phase error) and an upwind design where the level of dissipation can be specified by the designer.

πŸ“œ SIMILAR VOLUMES

A frequency accurate rth order spatial d
A frequency accurate rth order spatial derivative finite difference approximation
✍ Peter A. Orlin; A. Louise Perkins πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 202 KB

A method for the specification and design of finite difference spatial derivative approximations of general order r is presented. The method uses a difference polynomial with undetermined coefficients. Spatial frequency domain-based criteria, which include phase velocity, group velocity, and dissipa

Accurate Finite Difference Calculation O
Accurate Finite Difference Calculation Of The Natural Frequencies Of Euler-Bernoulli Beams Using Richardson Extrapolation
✍ F. OrduΓ±a-Bustamante πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 237 KB

A method is presented to obtain accurate estimations of the natural frequencies of nonuniform Euler-Bernoulli beams (the method can deal easily with all possible combinations of classical boundary conditions, including rotating and supporting end springs). The method is based on a repeated finite di

Finite-difference approximation for the
Finite-difference approximation for the u(k)-derivative with O(hMβˆ’k+1) accuracy: An analytical expression
✍ Vadim Dubovsky; Alexander Yakhot πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 105 KB

## Abstract An approximation of function __u__(__x__) as a Taylor series expansion about a point __x__~0~ at __M__ points __x__~__i__~, ∼ __i__ = 1,2,…,__M__ is used where __x__~__i__~ are arbitrary‐spaced. This approximation is a linear system for the derivatives __u__^(__k__)^ with an arbitrary a

Symbolic derivation of finite difference
Symbolic derivation of finite difference approximations for the three-dimensional Poisson equation
✍ Murli M. Gupta; Jules Kouatchou πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 307 KB πŸ‘ 2 views

A symbolic procedure for deriving various finite difference approximations for the three-dimensional Poisson equation is described. Based on the software package Mathematica, we utilize for the formulation local solutions of the differential equation and obtain the standard second-order scheme (7-po