Unformatted text preview: , x > 0 and w (0 , t ) = h ( t ) , t > . 5. (# 12.2.5 (a) and (d)) Solve using the method of characteristics: ∂w ∂t + c ∂w ∂x = e 2 x , w ( x, 0) = f ( x ) , and ∂w ∂t + 3 t ∂w ∂x = w, w ( x, 0) = f ( x ) , 6. (# 12.6.6 (a)) Consider the following tra±c ²ow problem: ∂ρ ∂t + c ( ρ ) ∂ρ ∂x = 0 . Assume that u ( ρ ) = u max (1 − ρ/ρ max ) and c ( ρ ) = d/dρ ( ρu ( ρ )). Solve for ρ ( x, t ) if ρ ( x, 0) = b ρ max , x < , x > . This initial condition corresponds to an inFnite line of tra±c stopped at a red light at x = 0 which is started by the light turning green. * MAP 4341; Instructor: Patrick De Leenheer. 1...
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- Summer '06
- Object-Oriented Programming, Boundary value problem, Green's function, Laplace's equation, Poisson's equation