research-article

Free access

Minimizing computer cost for the solution of certain scientific problems

Authors:

Gerald N. Pitts,

Paul B. Crawford,

Barry L. BatemanAuthors Info & Claims

AFIPS '70 (Fall): Proceedings of the November 17-19, 1970, fall joint computer conference

Pages 515 - 518

https://doi.org/10.1145/1478462.1478536

Published: 17 November 1970 Publication History

PDF eReader

Abstract

Many scientific problems require solution of the Laplace, Poission or Fourier equation. These equations occur in heat flow, fluid flow, diffusion and structural problems. It is well known that these types of problems lead to large sets of simultaneous equations that frequently require a number of iterations consuming a lot of computer dollars before a solution is obtained. Frequently one must solve a few hundred to a few thousand simultaneous equations. Numerical methods likely to be used for solution include: (1) Liebmann, an explicit method, (2) alternating direction implicit procedure and (3) banded matrix inversion technique.

References

[1]

G D Smith Numerical solution of partial differential equations Oxford University Press pp 149--151 1965

Google Scholar

[2]

J Douglas Jr On the numerical integration of μ_xx + μ_yy = μ_t by implicit methods J Soc Ind Appl Math Vol 3 pp 52--65 1955

Google Scholar

[3]

D W Peaceman H H Rachford Jr The numerical solution of parabolic and elliptic differential equations J Soc Ind Appl Math Vol 3 pp 28--44 1953

Google Scholar

[4]

B R Koehler Private Communication Texas A&M University College Station Texas March 10 1969

Google Scholar

[5]

B Carnahan H A Luther J O Wilkes The implicit alternating-direction method Applied Numerical Methods Vol 2 pp 543--553 1964

Google Scholar

Recommendations

The Reformulation and Numerical Solution of Certain Nonclassical Initial-Boundary Value Problems

Several physical phenomena are modeled by nonclassical parabolic or hyperbolic initial-boundary value problems in one space variable which involve an integral over the spatial domain of a function of the desired solution or of its first spatial ...
Numerical Solution of Boundary Value Problems in Differential-Algebraic Systems

This paper extends the theory of shooting and finite-difference methods for linear boundary value problems (BVPs) in ordinary differential equations (ODEs) to BVPs in differential-algebraic equations (DAEs) of the form \[ \begin{gathered} E(t)\mathcal{...
Numerical method for the solution of special nonlinear fourth-order boundary value problems

The sinc-Galerkin method is used to approximate solution of nonlinear problems. This work deals with the sinc-Galerkin method for solving nonlinear fourth-order differential equations with homogeneous and nonhomogeneous boundary conditions. The scheme ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

AFIPS '70 (Fall): Proceedings of the November 17-19, 1970, fall joint computer conference

November 1970

683 pages

ISBN:9781450379045

DOI:10.1145/1478462

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 17 November 1970

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

0
Total Citations
89
Total Downloads

Downloads (Last 12 months)14
Downloads (Last 6 weeks)3

Reflects downloads up to 20 Nov 2024

Other Metrics

View Author Metrics

Citations

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Recommendations

The Reformulation and Numerical Solution of Certain Nonclassical Initial-Boundary Value Problems

Numerical Solution of Boundary Value Problems in Differential-Algebraic Systems

Numerical method for the solution of special nonlinear fourth-order boundary value problems