2. Find a formal solution to the given initial-boundary value heat problem. Select two of the subprob- lems to complete. (a) homogeneous Dirichlet boundary heat problem U; = 5uxx, 0 0, u(t,0) = u(t,...


2. Find a formal solution to the given initial-boundary value heat problem. Select two of the subprob-<br>lems to complete.<br>(a) homogeneous Dirichlet boundary heat problem<br>U; = 5uxx, 0<x<1,t > 0,<br>u(t,0) = u(t, 1) = 0, t>0,<br>u(0, x) = (1 – x)x, 0<x<1.<br>(b) homogeneous Dirichlet boundary heat problem with source<br>U = 3uxx + x, 0<x<7, t >0<br>u(t,0) = u(1,7) =0, 1>0<br>u(0, x) = sin x, 0<x<A.<br>(c) non-homogeneous Dirichlet boundary heat problem<br>u = 2uxx 0<x<I,1>0<br>u(1,0) = 5, u(1, 71) = 10, t>0<br>u(0, x) = sin(3x) – sin(5.x), 0<x<<br>(d) homogeneous Neumann boundary heat problem<br>U = xx 0<x<A,1>0<br>u:(1,0) = u:(1, x) = 0, t>0<br>u(0, x) = e

Extracted text: 2. Find a formal solution to the given initial-boundary value heat problem. Select two of the subprob- lems to complete. (a) homogeneous Dirichlet boundary heat problem U; = 5uxx, 0<><1,t> 0, u(t,0) = u(t, 1) = 0, t>0, u(0, x) = (1 – x)x, 0<><1. (b)="" homogeneous="" dirichlet="" boundary="" heat="" problem="" with="" source="" u="3uxx" +="" x,=""><><7, t="">0 u(t,0) = u(1,7) =0, 1>0 u(0, x) = sin x, 00 u(0, x) = sin(3x) – sin(5.x), 0<>< (d)="" homogeneous="" neumann="" boundary="" heat="" problem="" u="xx">0 u(0, x) = e", 0<><>

Jun 04, 2022
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