Unformatted text preview: K ’s, and check that u i +1 can be written as the beginning of a Taylor series for y i +1 around x i . Deduce the order of accuracy of the scheme in this case from this calculation. 5. Consider a diﬀerence scheme of the form a 1 u i +1 + a u i + a1 u i1 + a2 u i2 = hf ( x i ,u i ), which is a consistent approximation of y = f ( x,y ) ( a 1 ,a ,a i1 , etc. are constants). Consider the polynomial P ( r ) = a 1 r i +1 + a r i + a1 r i1 + a2 r i2 . This polynomial always has r = 1 as a root. Explain why. 1...
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 Fall '08
 Rieffel
 Math, Numerical Analysis, Chorin, following diﬀerence schemes, initial initial value, standard fourthorder RK

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