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Knowledge
Milne’s Predictor–Corrector Method is a numerical approach used to solve Ordinary Differential Equations (ODEs) when analytical solutions are not available. This method employs previous values of the dependent variable and its derivative to predict and refine future values, enhancing accuracy. It relies on the combination of explicit and implicit formulas and is particularly effective for problems requiring high precision over discrete intervals.
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Sections
References
unit 5 ch7.pdfClass Notes
Memorization
What we have learnt
- Milne’s Predictor–Corrector...
- The method involves two mai...
- High accuracy is achieved t...
Final Test
Revision Tests
What we have learnt
- Milne’s Predictor–Corrector Method uses past values of y and f(x,y) for numerical solutions.
- The method involves two main steps: prediction using an explicit formula and correction using an implicit formula.
- High accuracy is achieved through the correction step, although it requires several initial values and can have limitations with stability in some cases.
Key Concepts
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Term: Milne’s Predictor–Corrector Method
Definition: A numerical method utilizing previous values to iteratively solve ODEs more accurately.
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Term: Predictor Formula
Definition: An explicit calculation to estimate the next value of y in the Milne's method.
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Term: Corrector Formula
Definition: An implicit calculation used to improve the estimate produced by the predictor formula.