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Solving PDEs with Initial & Boundary Conditions
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[QUOTE="Graham Power, post: 3861889, member: 408168"] [h2]Homework Statement [/h2] The PDE: ∂n/∂t + G∂n/∂L=0 The initial condition: n(0,L)=ns The boundary condition: n(t,0)=B/G The parameter B and G above are dependent upon process conditions and change at each time. They can be calculated with adequate experimental data. [h2]Homework Equations[/h2] I know that the characteristic equations for this PDE are: ∂n/∂s=0 (1) ∂L/∂s=G (2) ∂t/∂s=1 (3) Solving the above: n=n0 (4) t=s (5) L=Gt+L0 (6) [h2]The Attempt at a Solution[/h2] From what I can see, the above equations suggest that along a characteristic curve given by equation (6), the population density, n, at size L0, travels along the size axis with rate of growth, G. The initial condition, n(0,L)=ns describes the population of particles over a given size range. So the initial data I have is a number of values of population density, n, at a number of sizes. Does the solution suggest that each initial value of population density, n corresponding to an initial size, L0 will stay constant along equation (6) and correspond to a different size in the next time step? I hope I am clear in what I am saying here. [/QUOTE]
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Solving PDEs with Initial & Boundary Conditions
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