The automatic integration of ordinary differential equations

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Abstract
Cite
Gear, C. W. “The Automatic Integration of Ordinary Differential Equations”. Communications of the ACM, vol. 14, no. 3, 1971, pp. 176-9, https://doi.org/10.1145/362566.362571.
Gear, C. W. (1971). The automatic integration of ordinary differential equations. Communications of the ACM, 14(3), 176-179. https://doi.org/10.1145/362566.362571
Gear CW. The automatic integration of ordinary differential equations. Communications of the ACM. 1971;14(3):176-9.
Journal Categories
Science
Mathematics
Instruments and machines
Electronic computers
Computer science
Science
Mathematics
Instruments and machines
Electronic computers
Computer science
Computer software
Technology
Electrical engineering
Electronics
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Electronics
Computer engineering
Computer hardware
Description

Struggling with complex differential equations? This paper introduces a technique for automatically solving initial value problems for sets of ordinary differential equations. A key feature is a criterion for selecting the order of approximation, aiming to maximize step size and reduce solution time. The described criterion is based on the selection of the order of approximation. The program embodying the techniques includes an option for handling "stiff" differential equations. This automated approach streamlines the integration process, offering a valuable tool for scientists and engineers across diverse fields. The program embodying the techniques appears in Algorithm 407.

Published in Communications of the ACM, this article aligns with the journal's focus on computer science and programming. By presenting an algorithm for automatic integration, the paper contributes to the development of computational tools for solving mathematical problems relevant to computer science and other scientific domains.

Refrences
Citations
Citations Analysis
The first research to cite this article was titled Algorithm 407: DIFSUB for solution of ordinary differential equations [D2] and was published in 1971. The most recent citation comes from a 2024 study titled Algorithm 407: DIFSUB for solution of ordinary differential equations [D2] . This article reached its peak citation in 1981 , with 18 citations.It has been cited in 220 different journals, 5% of which are open access. Among related journals, the The Journal of Chemical Physics cited this research the most, with 12 citations. The chart below illustrates the annual citation trends for this article.
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