Derivation and comparison of predictor-corrector methods in the numerical solution of ordinary differential equations
The method of undetermined coefficients is used to derive the predictor-corrector equations for the second, third and fourth orders. The general form of equation of a multistep method is yn+1 = a y n-j + h j=1 bjf(xn-j,yn-j), where n = k. The derived equations give results that are satisf...
Saved in:
| Main Author: | |
|---|---|
| Format: | text |
| Language: | English |
| Published: |
Animo Repository
1985
|
| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/15993 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | De La Salle University |
| Language: | English |
| Summary: | The method of undetermined coefficients is used to derive the predictor-corrector equations for the second, third and fourth orders. The general form of equation of a multistep method is yn+1 = a y n-j + h j=1 bjf(xn-j,yn-j), where n = k. The derived equations give results that are satisfactory and better than the known method, that is, the Adams method. Predictor-corrector algorithm is also shown by approximating an ODE at certain point x. It is also proven that predictor-corrector pairs can be interchanged (e.g. Adams predictor with Milne's corrector). |
|---|