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Predictor-corrector procedures for systems of ordinary differential equations Zahar, Ramsay Vincent Michel
Abstract
Some of the most accurate and economical of the known numerical methods for solving the initial-value problem [Formula omitted] are of the predictor-corrector type. For systems of equations, the predictor-corrector procedures are defined in the same manner as they are for single equations. For a given problem and domain of t , a plot of the maximum error in the numerical approximation to x(t) obtained by a predictor-corrector procedure, versus the step-size, can be divided into three general regions - round-off, truncation, and instability. The most practical procedures are stable and have a small truncation error. The stability of a method depends on the magnitudes of the eigenvalues of a certain matrix that is associated with the matrix [Formula omitted] When the functions f[subscript i] are complicated, predictor-corrector procedures involving two evaluations per step seem to be the most efficient for general-purpose applications.
Item Metadata
Title |
Predictor-corrector procedures for systems of ordinary differential equations
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1964
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Description |
Some of the most accurate and economical of the known numerical methods for solving the initial-value problem
[Formula omitted]
are of the predictor-corrector type.
For systems of equations, the predictor-corrector procedures are defined in the same manner as they are for single equations.
For a given problem and domain of t , a plot of the maximum error in the numerical approximation to x(t) obtained by a predictor-corrector procedure, versus the step-size, can be divided into three general regions - round-off, truncation, and instability. The most practical procedures are stable and have a small truncation error.
The stability of a method depends on the magnitudes of the eigenvalues of a certain matrix that is associated with the matrix
[Formula omitted]
When the functions f[subscript i] are complicated, predictor-corrector procedures involving two evaluations per step seem to be the most efficient for general-purpose applications.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-10-31
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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 |
10.14288/1.0302286
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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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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.