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HW#7 - ChBE 521 Homework 7 due Wednesday November 11 1 How...

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ChBE 521 Homework 7 due Wednesday, November 11 1. How would you use finite differences to solve the boundary value problem in spherical coordinates d dr r 2 dc ( r ) dr = kc ( r ) subject to the boundary conditions c (1) = 1 , dc (0) dr = 0 . Solve the problem using N = 100. 2. Using finite differences ( N = 50), solve the partial differential equation ∂c ( t, x ) ∂t = 0 . 1 2 c ( t, x ) ∂x 2 + c ( t, x ) (1 + c ( x, t )) subject to the boundary conditions c ( t, 0) = 1 , c ( t, 1) = 2 , and the initial condition c (0 , x ) = 0. 3. Using collocation ( N = 10), solve the problem ∂c ( t, x ) ∂t = 0 . 1 2 c ( t, x ) ∂x 2 + c ( x, t ) subject to the boundary conditions ∂c ( t, 0) ∂x = 0 , ∂c ( t, 1) ∂x = 0 , and the initial condition c (0 , x ) = 1. 4. Using finite differences/Crank-Nicolson ( N = 100) and Strang splitting, solve the the partial differential equation ∂c ( t, x, y ) ∂t = 2 c ( t, x, y ) ∂x 2 + 2 2 c ( t, x, y ) ∂y 2 subject to the boundary conditions ∂c ( t, 0 , y ) ∂x
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