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 Problem: Adams bashforth predictor method y'=(x+y)/2,{{0,2},{0.5,2.636},{1,3.595},{1.5,4.968}},x=2 [ Calculator, Method and examples ]Solution:Your problem -> Adams bashforth predictor method y'=(x+y)/2,{{0,2},{0.5,2.636},{1,3.595},{1.5,4.968}},x=2y'=(x+y)/2Adam's Bashforth Predictor formula is y_(n+1,p) = y_n + h/24 (55y'_(n) - 59y'_(n-1) + 37y'_(n-2) - 9y'_(n-3))putting n=3, we gety_(4,p)=y_3 + h/24 (55y'_(3) - 59y'_2 + 37y'_1 - 9y'_0) ->(2)We have given thatx_0=0,x_1=0.5,x_2=1,x_3=1.5y_0=2,y_1=2.636,y_2=3.595,y_3=4.968y'=(x+y)/2y'_0=(x+y)/2=1 (where x=0,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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