Problem2.4.7 - Problem 2.4.7 The mathematical statement is...

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Problem 2.4.7 The mathematical statement is given by (1) 1 ÅÅÅÅ r ÅÅÅÅÅÅÅ r J r u ÅÅÅÅÅÅÅ r N + 1 ÅÅÅÅÅÅ r 2 2 u ÅÅÅÅÅÅÅÅÅ q 2 = 0, 0 < r < a, 0 < q < 2 p BC1 : u H a, q L = f H q L BC2 : » u H 0, q L » < ¶ BC3 : u H r, p L = u H r, -p L BC4 : u ÅÅÅÅÅÅÅ q H r, p L = u ÅÅÅÅÅÅÅ q H r, -p L Note that BC2 arises because at r = 0 is a singular point of the PDE and we require that the solution be finite. BC3 and BC4 simply state that the solution is continuous in q and 2 p periodic. The starting point for this problem is to assume the solution is separable., u H r, q L = G H r L f H q L . The eigenvalue problem for f is (2) 2 f ÅÅÅÅÅÅÅÅÅÅ „ q 2 = -l 2 f , BC3 : f H p L = f H -p L BC4 : f ÅÅÅÅÅÅÅ q H p L = f ÅÅÅÅÅÅÅ q H -p L The general solution is (3) f H q L = C 1 Cos H l q L + C 2 Sin H l q L If we apply BC3 we get (4) C 1 Cos H l p L + C 2 Sin H l p L = C 1 Cos H l p
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This note was uploaded on 02/18/2010 for the course ENGINEEING 32145 taught by Professor Stroeve during the Fall '09 term at Universidad de Carabobo.

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Problem2.4.7 - Problem 2.4.7 The mathematical statement is...

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