Re: Anyone here good at math, I has a math question ...
Posted by:
Mr. Nonethanesse
()
Date: April 06, 2022 10:58AM
5050man Wrote:
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> Need more clues.
The question is much further beyond that so there'd be no point in writing it down if you can only guess at the original one.
PDE: @u/@t = @u^2/@x^2 , 0<x<L 0<t<Infinity
IC: @u[0,t]/@x = @u[L,t]/@x = 0
BC: u[x,0] = f[x] , 0<x<L
While solving it comes to be that Tan[L*Subscript[\[Mu], n]] == -(Subscript[\[Mu], n]/\[Kappa]) are so called eigenvalues of the ODE BVP now at hand. For n = 0, 1, 2, ...
The question is: are these equal or approximately equal? "most books" (so i says) say they are exactly equal. But I don't think they are.
Integrate[Sin[Subscript[\[Mu], n]*x*L]*Sin[Subscript[\[Mu], m]*x*L], {x, 0, L}] = Integrate[Sin[Subscript[\[Mu], n]*x*L]^2, {x, 0, L}]
or
Integrate[Sin[Subscript[\[Mu], n]*x*L]*Sin[Subscript[\[Mu], m]*x*L], {x, 0, L}] ~ Integrate[Sin[Subscript[\[Mu], n]*x*L]^2, {x, 0, L}]