Unformatted text preview: solution). Is it possible to get higher accuracy by extrapolation? 2. Check that y = ( y i +1 + (3 / 2) y i3 y i1 + (1 / 2) y i2 ) / (3 h ) + O ( h 3 ) , where y i = y ( x i ). Write a program that implements the resulting scheme for solving y = f ( x,y ) ,y (0) = 1: u = 1 ,u 1 = u + hf (0 , 1) ,u 2 = u + 2 hf ( h,u 1 ) , and for i > 2, u i +1 =(3 / 2) u i +3 u i1(1 / 2) u i2 +3 f ( x i ,u i ). Use it to solve y =y,y (0) = 1, for 0 < x ≤ 2, with h = . 1 ,h = . 2. Comment on what you observe. 1...
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 Fall '08
 Rieffel
 Math, Numerical Analysis

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