Using the Notation from the Text, the Finite Difference Equation $y ^ { \prime \prime } + P ( x ) y ^ { \prime } + Q ( x ) y = f ( x ) , y ( a ) = \alpha , y ( b ) = \beta$

question 36

Multiple Choice

Using the notation from the text, the finite difference equation for solving the boundary value problem $y ^ { \prime \prime } + P ( x ) y ^ { \prime } + Q ( x ) y = f ( x ) , y ( a ) = \alpha , y ( b ) = \beta$ is

• A) \(\left( 1 - h P _ { i } / 2 \right) y _ { i + 1 } + \left( - 2 + h ^ { 2 } Q _ { i } \right) y _ { i } + \left( 1 + h P _ { i } / 2 \right) y _ { i - 1 } = h ^ { 2 } f _ { i }\)
• B) \(\left( 1 - h P _ { i } / 2 \right) y _ { i + 1 } + \left( - 2 + h ^ { 2 } Q _ { i } \right) y _ { i } + \left( 1 - h P _ { i } / 2 \right) y _ { i - 1 } = h ^ { 2 } f _ { i }\)
• C) \(\left( 1 + h P _ { i } / 2 \right) y _ { i + 1 } + \left( - 2 + h ^ { 2 } Q _ { i } \right) y _ { i } + \left( 1 + h P _ { i } / 2 \right) y _ { i - 1 } = h ^ { 2 } f _ { i }\)
• D) \(\left( 1 + h P _ { i } / 2 \right) y _ { i + 1 } + \left( 2 - h ^ { 2 } Q _ { i } \right) y _ { i } + \left( 1 - h P _ { i } / 2 \right) y _ { i - 1 } = h ^ { 2 } f _ { i }\)
• E) \(\left( 1 + h P _ { i } / 2 \right) y _ { i + 1 } + \left( - 2 + h ^ { 2 } Q _ { i } \right) y _ { i } + \left( 1 - h P _ { i } / 2 \right) y _ { i - 1 } = h ^ { 2 } f _ { i }\)

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