An Accelerated Iterative Procedure for Solving Partial Difference Equations of Elliptic Type

Doshi, Kishor Dharamsi; Ang, A.H-S.

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https://hdl.handle.net/2142/13772 Copy

Description

Title

An Accelerated Iterative Procedure for Solving Partial Difference Equations of Elliptic Type

Author(s)

• Doshi, Kishor Dharamsi
• Ang, A.H-S.

Issue Date

1962-04

Keyword(s)

• Acceleration scheme
• Partial differential equations

Abstract

This thesis deals with certain iterative methods of solving finite difference equations arising from elliptic type boundary-value problems. A procedure that accelerates the convergence of explicit) linear iterative methods of first degree is presented. The concept of acceleration implied here is similar to the one expressed in Hotelling's matrix squaring procedure in which the iterative sequence is advanced by a number of cycles at a time. Certain simplifying assumptions are made in the formulation of the acceleration scheme and as a result) some of the error components are diminished in the process) while others are magnified. A detailed study of the error and convergence associated with the acceleration scheme is presented. To substantiate the conclusions from analytical study) the procedure is studied in connection with the problem of plates on elastic foundation using the proposed scheme in conjunction with the successive over-relaxation method. The results clearly indicate the effectiveness of the procedure presented.

Publisher

University of Illinois Engineering Experiment Station. College of Engineering. University of Illinois at Urbana-Champaign.

Series/Report Name or Number

Civil Engineering Studies SRS-238

Type of Resource

text

Language

en

Permalink

http://hdl.handle.net/2142/13772

Sponsor(s)/Grant Number(s)

National Science Foundation Grant No. G-6572

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