Question
Asked Nov 7, 2019
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Solve the initial boundary value problem:
= a?uz
u(0,t) 0
r(1, t)hu(1, t) = 1
u(x, 0) = sin(Ta
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Solve the initial boundary value problem: = a?uz u(0,t) 0 r(1, t)hu(1, t) = 1 u(x, 0) = sin(Ta

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Expert Answer

Step 1

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Consider u (x,t) x(x)T (t) u(0,f)= x'(0)T ()0 Then, X'(0) 0 as T can't be 0 V all t и, (14)+ һu(1€) -1 x ()т()-һх()т() -1 1-пx (1)т() T (t)

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Step 2

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Two ODE are obtained T'(a T (t) and X" (x) x(x) with X'(0) 0 and = = గ 1-hx (1)T (t) x'(1) T (t)

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Advanced Math