= (1) (a) Discretize the 2D Poisson equation V?au(2, 3 ,y) Uxx + Uyy = -f(x, y) with second-order accurate central diffe

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1 A Discretize The 2d Poisson Equation V Au 2 3 Y Uxx Uyy F X Y With Second Order Accurate Central Diffe 1 (122.93 KiB) Viewed 50 times

= (1) (a) Discretize the 2D Poisson equation V?au(2, 3 ,y) Uxx + Uyy = -f(x, y) with second-order accurate central differences with Ax Ay = h. p(x,y) is the given charge density. (b) Express wij in terms of its four nearest neighbors and pij. (c) Write down the Jacobi iteration formula for u.+1) at iteration k +1 in terms of the four nearest neighbor values un at iteration k, plus p. (d) Define the residual rij = h2 · ((Vều)ij + pij). Then write the Jacobi method in terms of the residual (k) Finally write down the (e) Gauss-Seidel and (f) SOR iteration formulas for ,,(k+1) из Use the notation ř to denote the residual with current values ū of u (either updated or not) on the right-hand side. 7 ذه ۲