Solved: Approximate the solutions to the following elliptic partial differential
Chapter 12, Problem 3(choose chapter or problem)
Approximate the solutions to the following elliptic partial differential equations, using Algorithm 12.1: d 2 u d 2 u " ^ + ^= 0 ^ <1 - 1: u{x, 0) = 0, u{x, 1) = x, 0 < x < 1; h(0, y) = 0, m(1, y) = y, 0 < y < I. Use h k 0.2 and compare the results to the actual solution u{x, y) xy. d 2 ii d 2 u tc b. + =-(cos(x + })+ cos(x - y)). 0 < x < n, 0 < y < -] dxz dyz 2 u(0.y) = cosy, u(n, y) = - cos y, 0) = 3>ln 3', ?/(2, y) = 23'In^v), 1 < 3'< 2. Use h k OA and compare the results to the actual solution m(x, 3") = X3' lnx3'.
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