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Differential Equations Lecture Work Solutions 74

Differential Equations Lecture Work Solutions 74 - n = 0 X...

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-1 0 1 2 3 4 5 6 7 8 -2 -1 0 1 2 3 4 5 6 7 8 H u xx + uyy = 0 Figure 32: Sketch of domain 9. u y ( x, 0) = 0 u y ( x, H )=0 u (0 ,y )= f ( y ) X 0 λX =0 Y 0 + λY =0 solution should Y 0 (0) = 0 be bounded Y 0 ( H )=0 when x →∞ copy from table in Chapter 4 summary λ n = H 2 n =0 , 1 , 2 , ··· Y n =co s H y X 0 n H 2 X n =0 n =1 , 2 , ··· X n = A n e H x + B n e H x to get bounded solution A n =0
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Unformatted text preview: n = 0 X = 0 X = A x + B for boundedness A = 0 u = B Ā· 1 + āˆž X n =1 B n e āˆ’ n Ļ€ H x cos n Ļ€ H y u (0 , y ) = f ( y ) = B + āˆž X n =1 B n cos n Ļ€ H y Fourier cosine series of f ( y ). 74...
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