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Unformatted text preview: u ( x, t ). (d) Write a MATLAB program to compute solutions to this di²erential equation with c = 1 and boundary conditions u ( x, 0) = 0 , ∂u ∂t ( x, 0) = x + sin( πx ) . Submit plots of the solution at times t = 0 , . 5 , 1 . , 1 . 5 , 2 . 0. 2. [50 points] This question concerns the homogeneous wave equation on an unbounded spatial domain: ∂ 2 u ∂t 2 = ∂ 2 u ∂x 2 ,∞ < x < ∞ , t > . Find the solution u ( x, t ) to this equation with the following initial conditions: (a) u ( x, 0) = 2 sin( x ) ex 2 , ∂u ∂t ( x, 0) = 0; (b) u ( x, 0) = 0, ∂u ∂t ( x, 0) =2 x (1 + x 2 ) 2 ; (c) u ( x, 0) = 2 sin( x ) ex 2 , ∂u ∂t ( x, 0) =2 x (1 + x 2 ) 2 . (d) Produce a plot (or plots) showing your solution to part (c) over10 ≤ x ≤ 10 at times t = 0 , 1 , 2 , 3 , 4 , 5....
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This note was uploaded on 01/21/2012 for the course CAAM 330 taught by Professor Tompson during the Fall '09 term at UVA.
 Fall '09
 Tompson

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