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Unformatted text preview: MPO 662 – Problem Set 1 Feel free to use symbolic computation software such as mathematica or the symbolic toolbox in matlab to carry out the algebra 1. Find the characteristics of the following PDEs (a) u xx + 3 u xy + u yy = 0 (b) u xx- 2 u xy + u yy = 0 2. Consider the following PDE: ∂ ∂t + U ∂ ∂x ! 2 ψ- c 2 ∂ 2 ψ ∂x 2 = 0 where U and c are positive constants, and the first term is to be interpreted as: ∂ 2 ψ ∂t 2 + 2 U ∂ 2 ψ ∂x∂t + U 2 ∂ 2 ψ ∂x 2 • Classify this PDE • sketch the domain of dependence and the domain of influence in the x- t plane for the point ( x , t ). Consider the case U > c and U < c . 3. You can use a symbolic manipulator here to ease the algebra. Derive the following approximations to the first derivative at x = i Δ x : • 3 rd order upstream using the i- 2 , i- 1 , i and i + 1. • Derive a 4 th order centered approximations to the second derivative....
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This note was uploaded on 01/08/2012 for the course MPO 662 taught by Professor Iskandarani,m during the Spring '08 term at University of Miami.
- Spring '08