Consider the Problem a Finite Difference Approximation of the Solution Is Desired

question 10

Multiple Choice

Consider the problem $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial y ^ { 2 } } = 0 , u ( 0 , y ) = 0 , u ( x , 0 ) = 0 , u ( 1 , y ) = y - y ^ { 2 } , u ( x , 1 ) = x - x ^ { 2 }$ . A finite difference approximation of the solution is desired, using the approximation of the previous problem. Use a mesh size of $h = 1 / 3$ The conditions satisfied by the mesh points on the boundary are Select all that apply.

• A) \(u = 0\) at (0, 1/3) and (1/3, 0)
• B) \(u = 0\) at (0, 2/3) and (2/3, 0)
• C) \(u = 0\) at (1/3, 1/3) and (2/3, 2/3)
• D) \(u = 2 / 9\) at (1, 1/3) and (1/3, 1)
• E) \(u = 2 / 3\) at (1, 2/3) and (2/3, 1)

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