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Eq.(Q4-1) Question 4 (25 points) Consider the following heat equation Uxx(x,t) – ut(x,t) = 0, (0 < x < 10, 0

Posted: Mon May 09, 2022 11:02 am

by answerhappygod

Eq Q4 1 Question 4 25 Points Consider The Following Heat Equation Uxx X T Ut X T 0 0 X 10 0 T With T 1 (105.42 KiB) Viewed 21 times

Eq.(Q4-1) Question 4 (25 points) Consider the following heat equation Uxx(x,t) – ut(x,t) = 0, (0 < x < 10, 0 <t<) with the given boundary conditions u(0,t) = 0, u(10,t) = 0, (0<t < 0) and initial condition u(x,0) = f(x), (0 < x < 10) Eq.(Q4-2) Eq.(Q4-3) (a). (5 points) After calculations, u(x,t) can be expressed by the following series ηπα u(x,t) = En=1 Kn sin nit 2 10 10 where Kr's are some constants satisfying Eq.(Q4-1) and boundary conditions. Find an expression for K, such that u(x,t) also satisfies the initial condition. (b). (10 points) For f(x) = {16 – x, $ 5x<10 x, 0<x<5, Eq.(Q4-4) Find K, (C). (10 points) Now, if the original boundary conditions Eq.(Q4-2) are replaced by the following new ones: ux(0,t) = ux(10,t) = 0, (0 <t<0) Eq.(Q4-5) Find the solution u(x,t) satisfying boundary conditions Eq.(Q4-5) and initial condition Eq.(Q4-3).