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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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