3. Use the method of separation of variables to solve the problem Ut = xUxx x € [0, 1], t≥0, U (x, 0) = sinx, U (0, t) = 0, U.(t)-0. = Plot the solutions at several instants of time and describe in qualitative terms the behaviour of the solution to as too. What is lim→ U(x, t)? boundary conditions -Dirichlet to the left and (Observe that this problem has mixed Neumann to the right.)
3. Use the method of separation of variables to solve the problem Ut = xUxx x € [0, 1], t≥0, U (x, 0) = sinx, U (0, t) = 0, U.(t)-0. = Plot the solutions at several instants of time and describe in qualitative terms the behaviour of the solution to as too. What is lim→ U(x, t)? boundary conditions -Dirichlet to the left and (Observe that this problem has mixed Neumann to the right.)
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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![3. Use the method of separation of variables to solve the problem
Ut = xUxx x € [0, 1], t≥0,
U (x, 0) = sinx,
U (0, t) = 0,
U.(t)-0.
=
Plot the solutions at several instants of time and describe in qualitative terms the behaviour
of the solution to as too. What is lim→ U(x, t)?
boundary conditions -Dirichlet to the left and
(Observe that this problem has mixed
Neumann to the right.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81cabfe2-2c41-4796-8b8e-3ef5d3990a33%2F754d067f-fb5e-4735-8bdd-a65383dafb46%2Fctc7jzs_processed.png&w=3840&q=75)
Transcribed Image Text:3. Use the method of separation of variables to solve the problem
Ut = xUxx x € [0, 1], t≥0,
U (x, 0) = sinx,
U (0, t) = 0,
U.(t)-0.
=
Plot the solutions at several instants of time and describe in qualitative terms the behaviour
of the solution to as too. What is lim→ U(x, t)?
boundary conditions -Dirichlet to the left and
(Observe that this problem has mixed
Neumann to the right.)
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