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APM346-2018S
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Boundary condition
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Topic: Boundary condition (Read 756 times)
Ioana Nedelcu
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Boundary condition
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on:
February 05, 2018, 02:05:49 AM »
For section 2.6, question 1, how do we use the boundary condition at x = 0?
Solving using the initial conditions with d'Alembert's formula, the solution is $ u = \phi(x + ct) $, for x>ct and 0<x<ct since it has a positive argument always
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Victor Ivrii
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Re: Boundary condition
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Reply #1 on:
February 05, 2018, 04:13:42 AM »
D'Alembert formula does not give a correct solution for $0<x<ct$. You need to look at $u=\phi(x+ct)+\psi(x-ct)$ there
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Ioana Nedelcu
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Re: Boundary condition
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Reply #2 on:
February 05, 2018, 11:33:01 AM »
Right so here we would use the boundary condition at x=0 to find $\psi(x-ct)$ where the argument is negative (0<x<ct).
So $ u = \phi(x+ct) + \chi(\frac{t}{c}) - \phi(ct-x)$
Then I assume we use the initial conditions at t =0 to solve.
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Victor Ivrii
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Re: Boundary condition
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Reply #3 on:
February 05, 2018, 12:42:39 PM »
$\chi$ is needed to find $\psi$ for negative argument. Initial conditions were used already
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Toronto Math Forum
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APM346-2018S
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APM346––Home Assignments
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Boundary condition