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Find Milne's simpson predictor corrector method y'=(x+y)/2,{{0,0.5,1,1.5},{2,2.636,3.595,4.968}},x=2

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Your problem `->` Milne's simpson predictor corrector method y'=(x+y)/2,{{0,0.5,1,1.5},{2,2.636,3.595,4.968}},x=2


`y'=(x+y)/2`

Milne's simpson predictor formula is
`y_(n+1,p) = y_(n-3) + (4h)/3 (2y'_(n-2) - y'_(n-1)+ 2y'_(n))`

putting `n=3`, we get

`y_(4,p)=y_0 + (4h)/3 (2y'_1 - y'_2 + 2y'_3) ->(2)`

We have given that
`x_0=0,x_1=0.5,x_2=1,x_3=1.5`

`y_0=2,y_1=2.636,y_2=3.595,y_3=4.968`

`y'=(x+y)/2`

`y'_1=(x+y)/2=1.568` (where `x=0.5,y=2.636`)

`y'_2=(x+y)/2=2.2975` (where `x=1,y=3.595`)

`y'_3=(x+y)/2=3.234` (where `x=1.5,y=4.968`)

putting the values in (2), we get





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