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Consider the equation ut = Uxx, 0 < x < 1, t > 0, with boundary condition u(0, t) = 3, u(1, t) = 8, and initial condition u(x, 0) = cos(x). Setup we wish to change the problem into homogeneous boundary conditions. What is the steady state solution: Usteady state(x) = 5x+3 Let U (x, t) denote the transitent solution. That is, the solution of Ut = Uxx, 0 < x < 1, t> 0, with boundary condition U(0, t) = 0, U(1, t) 0, and initial condition. U (x,0) = e^x-5x-3 where the initial condition is such that u(x, t): = Usteady state(x) + U(x, t) solves the original problem above.

Consider the equation ut = Uxx, 0 < x < 1, t > 0, with boundary condition u(0, t) = 3, u(1, t) = 8, and initial condition u(x, 0) = cos(x). Setup we wish to change the problem into homogeneous boundary conditions. What is the steady state solution: Usteady state(x) = 5x+3 Let U (x, t) denote the transitent solution. That is, the solution of Ut = Uxx, 0 < x < 1, t> 0, with boundary condition U(0, t) = 0, U(1, t) 0, and initial condition. U (x,0) = e^x-5x-3 where the initial condition is such that u(x, t): = Usteady state(x) + U(x, t) solves the original problem above.

Advanced Engineering Mathematics
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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Consider the equation ut = Uxx, 0 < x < 1, t > 0, with boundary condition u(0, t) = 3, u(1, t) = 8, and initial condition u(x,0) = cos(x). Setup we wish to change the problem into homogeneous boundary conditions. What is the steady state solution: Usteady state (x) - Let U (x, t) denote the transitent solution. That is, the solution of Ut = Uxx, 0 < x < 1, t > 0, with boundary condition U(0, t) = 0, U(1, t) = 0, and initial condition e^x-5x-3 U(x, 0) = = = 5x+3 where the initial condition is such that Usteady state(x) + U(x, t) solves the original problem above. u(x, t) =
Transcribed Image Text:Consider the equation ut = Uxx, 0 < x < 1, t > 0, with boundary condition u(0, t) = 3, u(1, t) = 8, and initial condition u(x,0) = cos(x). Setup we wish to change the problem into homogeneous boundary conditions. What is the steady state solution: Usteady state (x) - Let U (x, t) denote the transitent solution. That is, the solution of Ut = Uxx, 0 < x < 1, t > 0, with boundary condition U(0, t) = 0, U(1, t) = 0, and initial condition e^x-5x-3 U(x, 0) = = = 5x+3 where the initial condition is such that Usteady state(x) + U(x, t) solves the original problem above. u(x, t) =
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