Problem 10. (8 points) Consider the following PDE: at +20T - 4T = x - 2y Ox? dy Suppose the domain of the above PDE is a

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Problem 10 8 Points Consider The Following Pde At 20t 4t X 2y Ox Dy Suppose The Domain Of The Above Pde Is A 1 (42.85 KiB) Viewed 14 times

Problem 10. (8 points) Consider the following PDE: at +20T - 4T = x - 2y Ox? dy Suppose the domain of the above PDE is a rectangle 0 sxsa and Os y s b, and it is discretized into a regular gird with nodes (x, y) = (ih, j·l), i = 0, 1, 2, ..., m, and j = 0, b 1, 2, ..., n, where m and n for some integers m and n. Let T, = T(x, y). h=4 12 Use the Centered Difference Formula to give the Finite Difference Equation of this PDE in terms of T at node (x, y) and nearby nodes and, i, j, h, and I. (Note: U(x + Ar)- U(x - Ar) 2Ar The 1"-order centered difference of a U(x) at x is U(x + Ar)- 2U(x)+U(r - Ar) (Ar) The 2"-order centered difference of a U(x) at x is )