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Syntactically Concise Gaussian Double Integration for Apl

IP.com Disclosure Number: IPCOM000039067D
Original Publication Date: 1987-Apr-01
Included in the Prior Art Database: 2005-Feb-01
Document File: 1 page(s) / 11K

Publishing Venue

IBM

Related People

Moyer, TP: AUTHOR

Abstract

A computer programming technique has been developed to perform a double integration using Gaussian integration number sets. The novel features are to consider the outer integration first and to evaluate the function using each Gaussian number while simultaneously using the same number as one of the limits of integration. The following steps are the key elements in this integration: 1. Denormalize the Gaussian integration points (a set of known universal numbers) into the integration bounds on the variable over which integrating is being done. 2. Evaluate the function to be integrated at each of the denormalized Gaussian integration points. 3.

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Syntactically Concise Gaussian Double Integration for Apl

A computer programming technique has been developed to perform a double integration using Gaussian integration number sets. The novel features are to consider the outer integration first and to evaluate the function using each Gaussian number while simultaneously using the same number as one of the limits of integration. The following steps are the key elements in this integration: 1. Denormalize the Gaussian integration points

(a set of known universal numbers) into the

integration bounds on the variable over which

integrating is being done.

2. Evaluate the function to be integrated at

each of the denormalized Gaussian integration

points.

3. Pair the results of the above evaluations

with a second set of known universal numbers.

Multiply the members of each pair together

and sum the products. Renormalize, and the

answer is evident. To perform a Gaussian double integration, the concept of considering the outer integration first must be used. By using the outer integration first, the function to be integrated is, itself, an integration; specifically it is the inner integration. The techniques can also be applied to triple- and higher-order integrations.

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