𝔖 Bobbio Scriptorium
✦   LIBER   ✦

An analysis of alternating-direction methods for parabolic equations

✍ Scribed by Michael A. Celia; George F. Plnder

Publisher
John Wiley and Sons
Year
1985
Tongue
English
Weight
544 KB
Volume
1
Category
Article
ISSN
0749-159X

No coin nor oath required. For personal study only.

✦ Synopsis

Alternating-direction solution procedures for parabolic partial differential equations can be developed using finite-difference, finite-element, and collocation approximations in space. Each of these methods derives from a common alternating-direction formulation. Furthermore, each method leads to an O[(Ar)'] error which is in addition to the discretization error associated with standard multidimensional solutions. However, when dealing with equations having spatially varying coefficients, some alternating-direction formulations lead to yet other errors which are O(At). These latter errors, and thus the accuracy of the method, depend on the structure of the mass matrix associated with the approximating met hod. Numerical Methods for Partial Differential Equations, I , 57-70 (1985) 0 1985 John Wiley & Sons, Inc.

πŸ“œ SIMILAR VOLUMES

Generalized alternating-direction colloc
Generalized alternating-direction collocation methods for parabolic equations. II. Transport equations with application to seawater intrusion problems
✍ Michael A. Celia; George F. Pinder πŸ“‚ Article πŸ“… 1990 πŸ› John Wiley and Sons 🌐 English βš– 641 KB

## Abstract The alternating‐direction collocation (ADC) method combines the attractive computational features of a collocation spatial approximation and an alternating‐direction time marching algorithm. The result is a very efficient solution procedure for parabolic partial differential equations.

An Alternating Direction Implicit Scheme
An Alternating Direction Implicit Scheme for Parabolic Equations with Mixed Derivative and Convective Terms
✍ S. McKee; D.P. Wall; S.K. Wilson πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 474 KB

THIS PAPER IS DEDICATED TO PROFESSOR A. R. MITCHELL ON THE EVENT OF HIS 75TH BIRTHDAY ## 2. PHYSICAL BACKGROUND AND MOTIVATION An alternating direction implicit (ADI) scheme is introduced which ### 2.1. Problem Formulation is capable of solving a general parabolic equation in two space dimension