𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A frequency accurate rth order spatial derivative finite difference approximation

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

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
202 KB
Volume
15
Category
Article
ISSN
0749-159X

No coin nor oath required. For personal study only.

✦ Synopsis

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 dissipation requirements at a priori selected spatial frequencies, are used to find the appropriate coefficient values. The method is formulated as an optimal design problem but is pursued heuristically. The general derivative approximation and the design method are suitable for use in more general design problems involving finite difference schemes for linear and nonlinear partial differential equations.

📜 SIMILAR VOLUMES

A frequency accurate spatial derivative
A frequency accurate spatial derivative finite difference approximation
✍ Peter A. Orlin; A. Louise Perkins; George Heburn 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 163 KB

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

A fourth-order accurate, Numerov-type, t
A fourth-order accurate, Numerov-type, three-point finite-difference discretization of electrochemical reaction-diffusion equations on nonuniform (exponentially expanding) spatial grids in one-dimensional space geometry
✍ Lesław K. Bieniasz 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 117 KB 👁 1 views

## Abstract The validity for finite‐difference electrochemical kinetic simulations, of the extension of the Numerov discretization designed by Chawla and Katti [J Comput Appl Math 1980, 6, 189–196] for the solution of two‐point boundary value problems in ordinary differential equations, is examined