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Author Brans, Carl H.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1967
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract A program is described which enables a digital computer to perform the formal algebraic manipulations and differentiations required to test a set of algebraic partial differential equations for consistency, and, if the set is consistent, to reduce the equations in it to such an extent that the nature of the arbitrary functions uniquely generating all local, analytic solutions is apparent upon inspection. The computer performs these operations on polynomials in a nonnumerical sense, treating variables and derivatives of variables precisely as they are treated in the symbolic operations of algebra and calculus. The language which permits the computer to deal with variables and polynomials in this fashion is described. The general mathematical problem of testing and reduction of sets of algebraic partial differential equations is briefly described together with the techniques available for resolving it as adapted to this computer language. A brief description of the FORTRAN program itself is also given. The motivation for the development of this program was the study of the Einstein gravitational equations in general relativity. It has been shown that these equations can be invariantly reduced to a finite number of sets of algebraic partial differential equations, and the problem of testing and reducing these sets led to this program. The program reported on in this paper has been successfully tested for comparatively simple problems, some of which are described here, but must be further developed for the relativity applications.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1967-01-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 14
Issue Number 1
Page Count 18
Starting Page 45
Ending Page 62

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Source: ACM Digital Library