| 1 |
Note these are essentially interpolation formulae for if one uses information from m t values, you can fit a degree m-1 polynomial
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| 2 |
Taylor expansion and Polynomial fitting are essentially the same thing!
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| 3 |
Implicit Multistep Methods are gotten using backwards difference interpolating polynomials starting at ti+1. But wherever we we need f(ti+1,y(ti+1)), we use f(ti+1, X*i+1) where X*i+1is derived from the explicit predictor equation
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| 4 |
Note that implicit formulae should be best as explicit method involves extrapolation from ti to ti+1 whereas in implicit case ti+1 is endpoint of region in which interpolation done
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| 5 |
Extrapolation is always unreliable and to be avoided!
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