Differential Equations Lecture Work Solutions 123

Differential Equations Lecture Work Solutions 123 - ( + ) Z...

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4. u xx + u yy + u zz =0 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, W )=0 X 0 X + Y 0 Y + Z 0 Z =0 u ( x, y, 0) = 4 cos 3 π L x cos 4 π L y 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 x n =0 , 1 , 2 ··· Y 0 + µY =0 BC : Y 0 (0) = Y 0 ( L )=0 µ m = L 2 Y m =co s L y m =0 , 1 , 2 ··· Z 0
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Unformatted text preview: ( + ) Z = 0 Z ( W ) = 0 Z ( n L ) 2 + ( m L ) 2 Z = 0 Z nm = cosh s n L 2 + m L 2 ( z W ) 123...
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