HW_09_Solutions

# HW_09_Solutions - A Problem 1 Linear BVP based on the...

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Unformatted text preview: A. Problem 1. Linear BVP based on the central differences- y 00 + (1- x ) y = x, ≤ x ≤ 1 , y (0) = y (1) = 2 p ( x ) = 0 , q ( x ) = 1- x, f ( x ) = x h = 0 . 25 x = 0 , x 1 = 0 . 25 , x 2 = 0 . 5 , x 3 = 0 . 75 , x 4 = 1 Four intervals = ⇒ n = 4, It becomes a problem of 3 (= n-1) equations with 3( = n-1) unknowns (TU = F). t i,i- 1 =- 1 + 1 2 p i h , t i,i = ( 2 + q i h 2 ) , t i,i +1 =- 1- 1 2 p i h t 1 , 1 = ( 2 + (1- x 1 ) h 2 ) = 2+(1 = 0 . 25) · . 25 2 = 2 . 0469 , t 1 , 2 =- 1- 1 2 · · h =- 1 , t 1 , 3 = 0 t 2 , 1 =- 1 + 1 2 · · h 2 =- 1 , t 2 , 2 = 2 . 0133 , t 2 , 3 =- 1 t 3 , 1 = 0 , t 3 , 2 =- 1 , t 3 , 3 = 2 . 0156 F 1 = 1 + 1 2 p 1 h g + h 2 f 1 = 1 + 1 2 · · h · 2 + 0 . 25 2 · . 25 = 2 . 0156 F 2 = h 2 f 2 = 0 . 25 2 · . 50 = 0 . 0313 F 3 = 1- 1 2 p 3 h g 1 + h 2 f 3 = 2 . 0469 , where g = y ( x ) = 2 , g 1 = y ( x n ) = 2 T U = F = ⇒ 2 . 0469- 1- 1 2 . 0313- 1- 1 2 . 0156 y 1 y 2 y 3...
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HW_09_Solutions - A Problem 1 Linear BVP based on the...

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