Solution of a scaled system via generalized orthogonal polynomials
作者:
RONG-YEU CHANG,
SHWU-YIEN YANG,
MAW-LING WANG,
期刊:
International Journal of Systems Science
(Taylor Available online 1987)
卷期:
Volume 18,
issue 12
页码: 2369-2382
ISSN:0020-7721
年代: 1987
DOI:10.1080/00207728708967193
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
Generalized orthogonal polynomials which include all types of orthogonal polynomial are introduced first. Using the idea of orthogonal polynomials that can be expressed by a Taylor power series and vice versa, the operational matrix for the integration of the generalized orthogonal polynomials is first derived. A stretched operational matrix of diagonal form is also derived. Both the operational matrix for the integration and the stretched operational matrix of generalized orthogonal polynomials are applied to solve functional differential equations. The characteristics of each kind of orthogonal polynomial in solving the scaled system is demonstrated. The computational strategy for finding the expansion coefficients of the state variables is very simple, straightforward and easy. The inversion of only one matrix, which has the same dimension as the state variables, is required. The expansion coefficients of the state variables are obtained by the proposed recursive formula. Much computer time is thus saved and computational results are obtained that are very accurate compared with previous methods.
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