Solve Laplace's equation, u(x, y) = where A u(0, y) = F(y), u(x, 0) = 0,...

 

Transcribed Image Text:

Solve Laplace's equation, u(x, y) = where A u(0, y) = F(y), u(x, 0) = 0, + 8²u + = 0, 0 < x <a, 0 < y < b, (see (1) in Section 12.5) for a rectangular plate subject to the given boundary conditions. ax² ay² u(a, y) = u(x, b) = 0 00 n = 1 A G(y) () + B₁ ( 1 = - Winnity(b* of sinh = 3 / * F(y) sin(y) dy and B- G(y) sin(ny) dy - A, cosh (Ta)) Solve Laplace's equation, u(x, y) = where A u(0, y) = F(y), u(x, 0) = 0, + 8²u + = 0, 0 < x <a, 0 < y < b, (see (1) in Section 12.5) for a rectangular plate subject to the given boundary conditions. ax² ay² u(a, y) = u(x, b) = 0 00 n = 1 A G(y) () + B₁ ( 1 = - Winnity(b* of sinh = 3 / * F(y) sin(y) dy and B- G(y) sin(ny) dy - A, cosh (Ta))