Solve Poisson equation V²V = −ps/ɛ, 0≤x≤5, 0≤ y ≤ 5, assuming that there are insulating gaps at the corners of the recta

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Solve Poisson equation V²V = −ps/ɛ, 0≤x≤5, 0≤ y ≤ 5, assuming that there are insulating gaps at the corners of the rectangular region and subject to boundary conditions u(0, y) = 0, u(5, y) = sin(y) u(x, 0) = x, u(x, 5) = -3 for Er = 9 and {(x - 5) x 1² = {0- [(y−5)x [nC/m²] 1≤x≤4,1≤y≤4 Ps elsewhere Use FD equations for elliptic PDEs and compare the results with analytic exact solution. To do this a) Choose x=constant and plot variation of u(x, y) with respect to y for both analytical and numerical calculation. b) Choose y constant and plot variation of u(x, y) with respect to x for both analytical and numerical calculation. c) Plot 2D spatial variation for both analytical and numerical calculation. d) Define a relative error function considering all nodes to show the validity of FD equations quantitatively.