Laplaces equation in polar coordinates, Eq (8 11), is complicated by the variable radius r Consider the finite difference mesh in Fig P8 106, with nodes (i, j) at equally spaced Delta theta and Delta r Derive a finite difference model for Eq (8 11) similar to our Cartesian expression in Eq (8 109) i,j 1 Vo i j Ar

Question: Laplaces equation in polar coordinates, Eq. (8.11), is complicated by the variable radius r. Consider the finite difference mesh in Fig. P8.106, with nodes (i,

Laplace€™s equation in polar coordinates, Eq. (8.11), is complicated by the variable radius r. Consider the finite difference mesh in Fig. P8.106, with nodes (i, j) at equally spaced Δθ and Δr. Derive a finite-difference model for Eq. (8.11) similar to our Cartesian expression in Eq. (8.109).

Laplace€™s equation in polar coordinates

i,j+1 Vo i.j Ar

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