Solve the Poisson equation ∇^2u = sin(πx) for 0 ≤ x ≤ 1and 0 ≤ y ≤ 1 with boundary conditions u(x, 0) = x for 0 ≤ x ≤ 1/2,

Question

u(x, 0) = 1 − x for 1/2 ≤ x ≤ 1 and 0 everywhere else. Hint: break this up as
into two different PDEs.

Answer 1

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