Partial Differential Equations : Eigenvalue Expansion
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Solve the Boundary value problem
PDF: Ut = Uxx + 7sin(5x/2)
b. C. U(0,t) = 3
Ux(Pi,t) = 0
i. c. U(x,0) = 3 + 6sin(7x/2)
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A boundary value problem is solved using an eigenvalue expansion. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
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Solve the Boundary value problem
PDF: Ut = Uxx + 7sin(5x/2)
b. C. U(0,t) = 3
Ux(Pi,t) = 0
i. c. U(x,0) = 3 + 6sin(7x/2)
We start with converting the boundary conditions to periodic boundary conditions.
Introducing the new function v(x,t) we get:
Also, note that:
Therefore the new system is:
The second step is to find the homogenous solution for the equation:
Using the method of separation of variables we set:
Substituting this ...
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