Komputasi untuk Sains dan Teknik - Universitas Indonesia

8.5. LATIHAN 149u (x i , t 1 ) = u (x i , 0) + kg (x i ) + α2 k 2w i1 = w i0 + kg (x i ) + α2 k 22 f” (x i) + k36∂ 3 u∂t 3 (x i, ˆµ i ) (8.45)2 f” (x i) (8.46)f” (x i ) = f (x i+1) − 2f (x i ) + f (x i−1 )h 2− h2 )f(4)(˜ξ12(8.47)u (x i , t 1 ) = u (x i , 0) + kg (x i ) + k2 α 22h 2 [f (xi+1 ) − 2f (x i ) + f (x i−1 )h 2] + O ( k 3 + h 2 k 2) (8.48)u (x i , t 1 ) = u (x i , 0) + kg (x i ) + λ22[f (xi+1 ) − 2f (x i ) + f (x i−1 )h 2] + O ( k 3 + h 2 k 2) (8.49)= ( 1 − λ 2) f (x i ) + λ22 f (x i+1) + λ22 f (x i−1) + kg (x i ) + O ( k 3 + h 2 k 2) (8.50)w i,1 = ( 1 − λ 2) f (x i ) + λ22 f (x i+1) + λ22 f (x i−1) + kg (x i ) (8.51)