Suppose we have a bar of length L = 2 and, instead of keeping the ends at a constant 0°C the bar has insulated ends. We can model this situation with the following boundary conditions: 1. Uz(0, t) = 0 , Uz(2, t) = 0 (a) Show that the boundary condition uz(0, t) implies X'(0) = 0 or T(t) = 0. (b) Fill in the blanks: The boundary condition u(2, t) = 0 implies = 0 or *0 = (c) This leads us to the boundary value problem with parameter: X" + XX = 0, X'(0)= 0, X'(2) = 0 Find the nontrivial solutions to the BVP for the case where A> 0. Assume = u2. Recall that sin 0 = 0 for 0 = nK.

Suppose we have a bar of length L = 2 and, instead of keeping the ends at a constant 0°C the bar has insulated ends. We can model this situation with the following boundary conditions: 1. Uz(0, t) = 0 , Uz(2, t) = 0 (a) Show that the boundary condition uz(0, t) implies X'(0) = 0 or T(t) = 0. (b) Fill in the blanks: The boundary condition u(2, t) = 0 implies = 0 or *0 = (c) This leads us to the boundary value problem with parameter: X" + XX = 0, X'(0)= 0, X'(2) = 0 Find the nontrivial solutions to the BVP for the case where A> 0. Assume = u2. Recall that sin 0 = 0 for 0 = nK.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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