Differential Equations Lecture Work Solutions 160

Differential Equations Lecture Work Solutions 160 - = u x L...

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5.4 Poisson’s Equation 5.4.1 Homogeneous Boundary Conditions 5.4.2 Inhomogeneous Boundary Conditions Problems 1. Solve 2 u = S ( x, y ) , 0 <x<L , 0 <y<H, a. u (0 ,y )= u ( L, y )=0 u ( x, 0) = u ( x, H )=0 Use a Fourier sine series in y. b. u (0 ,y )=0 u ( L, y )=1 u ( x, 0) = u ( x, H )=0 Hint: Do NOT reduce to homogeneous boundary conditions. c. u x (0
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Unformatted text preview: ) = u x ( L, y ) = 0 u y ( x, 0) = u y ( x, H ) = 0 In what situations are there solutions? 2. Solve the following Poisson’s equation ∇ 2 u = e 2 y sin x, < x < π, < y < L, u (0 , y ) = u ( π, y ) = 0 , u ( x, 0) = 0 , u ( x, L ) = f ( x ) . 160...
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