1. Solve the Laplace equation in two dimensions and in rectilinear coordinates x, y: 8 8...

Transcribed Image Text:

1. Solve the Laplace equation in two dimensions and in rectilinear coordinates x, y: 8² 8² x(x,y) + zu(x,y) = 0 subject to the boundary conditions given. Provide contour plot(s) of your solution. (a) u(0, y) = u(1. y) = 0 and u(x,0) = u(x, L) = F(x) = sin mx -sin 3x + sin 5mx. L is some positive real number. Provide contour plots for L= 0.3 and L = 3. 1. Solve the Laplace equation in two dimensions and in rectilinear coordinates x, y: 8² 8² x(x,y) + zu(x,y) = 0 subject to the boundary conditions given. Provide contour plot(s) of your solution. (a) u(0, y) = u(1. y) = 0 and u(x,0) = u(x, L) = F(x) = sin mx -sin 3x + sin 5mx. L is some positive real number. Provide contour plots for L= 0.3 and L = 3.