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. |
Page generated in 0.0105 seconds