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. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/38429 |
| Date | January 1964 |
| Creators | Zahar, Ramsay Vincent Michel |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| 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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