Consider the Boundary-Value Problem $y ^ { \prime \prime } - 4 y ^ { \prime } + 3 y = x , y ( 0 ) = 1 , y ( 1 ) = 2$

question 11

Multiple Choice

Consider the boundary-value problem $y ^ { \prime \prime } - 4 y ^ { \prime } + 3 y = x , y ( 0 ) = 1 , y ( 1 ) = 2$ . Replace the derivatives with central differences with a step size of $h = 1 / 4$ . The resulting equations are

• A) \(12 y _ { i + 1 } - 29 y _ { i } - 24 y _ { i - 1 } = x _ { i }\)
• B) \(12 y _ { i + 1 } + 17 y _ { i } + 12 y _ { i - 1 } = x _ { i }\)
• C) \(8 y _ { i + 1 } + 17 y _ { i } + 12 y _ { i - 1 } = x _ { i }\)
• D) \(8 y _ { i + 1 } - 29 y _ { i } + 24 y _ { i - 1 } = x _ { i }\)
• E) \(8 y _ { i + 1 } + 29 y _ { i } - 24 y _ { i - 1 } = x _ { i }\)

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