Differential quadrature for multi-dimensional problems
type: Item
instance of: scholarly article
title: Differential quadrature for multi-dimensional problems
zbMATH Open document ID: 0557.65084
DOI: 10.1016/0022-247X(84)90111-2
author: Faruk Civan
author: C. M. Sliepcevich
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: This paper uses a technique developed by R. E. Bellman and his coworkers and applies a generalisation of this technique to the solution of time dependent and time independent partial differential equations involving multiple space dimensions. This technique involves an approximation of the form \((\partial^ m/\partial x^ m)f(x_ i)\simeq \sum^{N}_{j=1}W_{ij}f(x_ j)\) where the data points \(x_ i\) are given and the weights are chosen so that the result is exact when \(f(x)=x^ k\), \(k=0,...,(N-1)\). For the time independent case the theory leads to a set of linear algebraic equations for the values of the solution at the grid points. The time dependent case leads to a similar set of linear first order differential equations in time. Examples and numerical computations are given using convection-diffusion equations.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 3888864
zbMATH Keywords: differential quadrature
zbMATH Keywords: convection-diffusion equation
zbMATH Keywords: steady-state dispersion of inert, neutrally buoyant pollutants
zbMATH Keywords: unbounded atmosphere
reviewed by: Brian L. Burrows
MaRDI profile type: Publication
cites work: Methods of nonlinear analysis. Vol. II
cites work: Differential quadrature and longterm integration
cites work: Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations
cites work: Solution of the partial differential equation of the Hodgkin-Huxley model using differential quadrature
cites work: Systems identification with partial information
cites work: A scanning technique for systems identification
cites work: Application of differential quadrature to transport processes
cites work: Solution of the Poisson equation by differential quadrature
cites work: Q5535370
cites work: Q5678345
cites work: Computational considerations in non‐linear diffusion
cites work: The method of differential quadrature for transient nonlinear diffusion
cites work: A high-order accurate numerical algorithm for three-dimensional transport prediction
cites work: Solving $Ax = b$: A Method with Reduced Storage Requirements
full work available at URL: 0022-247x(84)90111-2
OpenAlex ID: W1987313489
description: scientific article; zbMATH DE number 3888864