Question: For the coordinate transformation (12.1) and (12.2), develop the second-order finite difference approximations of (u_{y}, u_{x x}), and (u_{x y}) at (left(xi_{i}, eta_{j} ight)). Apply

For the coordinate transformation (12.1) and (12.2), develop the second-order finite difference approximations of $u_{y}, u_{x x}$, and $u_{x y}$ at $\left(\xi_{i}, \eta_{j}\right)$. Apply central differences for discretization of derivatives with respect to $\xi$ and $\eta$.

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