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An application of linear analysis to initial value problems Law, Alan Greenwell
Abstract
Certain properties of an unknown element u in a Hilbert space are investigated. For u satisfying certain linear constraints, it is shown that approximations to u and error bounds for the approximations may be obtained in terms of functional representers. The general approximation method is applied to homogeneous systems of ordinary linear differential equations and various formulae are derived. An Alwac III-E digital computer was used to compute optimal approximations and error bounds with the aid of these formulae. Numerous applications to particular systems are mentioned. On the basis of the numerical results, certain remarks are given as a guide for the numerical application of the method, at least in the framework of ordinary differential equations. From the cases studied it is seen that this can be a practicable method for the numerical solution of differential equations.
Item Metadata
Title |
An application of linear analysis to initial value problems
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1961
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Description |
Certain properties of an unknown element u in a Hilbert space are investigated. For u satisfying certain linear constraints, it is shown that approximations to u and error bounds for the approximations may be obtained in terms of functional representers.
The general approximation method is applied to homogeneous systems of ordinary linear differential equations and various formulae are derived. An Alwac III-E digital computer was used to compute optimal approximations and error bounds with the aid of these formulae.
Numerous applications to particular systems are mentioned. On the basis of the numerical results, certain remarks are given as a guide for the numerical application of the method, at least in the framework of ordinary differential equations. From the cases studied it is seen that this can be a practicable method for the numerical solution of differential equations.
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Genre | |
Type | |
Language |
eng
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Date Available |
2012-01-24
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080644
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.