Differential Equations Lecture Work Solutions 121

Differential Equations Lecture Work Solutions 121 - Z ( + )...

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3. u xx + u yy + u zz =0 BC : u x (0 ,y ,z )=0 u x ( L, y, z )=0 u y ( x, 0 ,z )=0 u y ( x, L, z )=0 u ( x, y, 0) = 4 cos 3 π L x cos 4 π L y u ( x, y, z )= X ( x ) Y ( y ) Z ( z ) X 0 X + Y 0 Y + Z 0 Z =0 X 0 X = Y 0 Y Z 0 Z = λ X 0 + λX =0 BC : X 0 (0) = X 0 ( L )=0 λ n = L 2 X n =co s L xn =0 , 1 , 2 ··· Y 0 Y = λ Z 0 Z = µ Y 0 + µY =0 BC : Y 0 (0) = Y 0 ( L )=0 µ n = L 2 Y m =co s L ym =0 , 1 , 2 ··· Z 0 Z = λ + µ
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Unformatted text preview: Z ( + ) Z = 0 BC : Z ( W ) = 0 Z " n L 2 + m L 2 # Z = 0 Z nm = sinh s n L 2 + m L 2 ( z W ) 121...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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