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Question: How to change summation index of Sum from PDE solution?

Question:How to change summation index of Sum from PDE solution?

Mariusz Iwaniuk 1526 Maple 2016
sum eval subs
December 12 2016
1

Hello.

I have a Pde solution in from of the sum.

pde := diff(u(x, t), t) = diff(u(x, t), x$2)

symbolic := pdsolve([pde, u(x, 0) = 1, u(0, t) = 0, u(1, t) = 0])

symbolic := u(x, t) = Sum(-(2*((-1)^_Z9-1))*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

 

I tried a subs or eval command dosen't work.

 

Thanks.

pdex1.mw
 

> 

restart
> 

pde := diff(u(x, t), t) = diff(u(x, t), `$`(x, 2)):
> 

ics := [u(x, 0) = 1, u(0, t) = 0, u(1, t) = 0]:
> 

pds := pdsolve(pde, ics, numeric, time = t, range = 0 .. 1, spacestep = 1/4024, timestep = 1/4024):
> 

symbolic := pdsolve([pde, u(x, 0) = 1, u(0, t) = 0, u(1, t) = 0])

u(x, t) = Sum(-2*((-1)^_Z9-1)*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

 (1)
> 

eval(rhs(symbolic), `~`[_Z9] = n)

Sum(-2*((-1)^_Z9-1)*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

 (2)
> 

subs(`~`[_Z9] = n, rhs(symbolic))

Sum(-2*((-1)^_Z9-1)*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

 (3)
> 

subs[eval](`~`[_Z9] = n, rhs(symbolic))

Sum(-2*((-1)^_Z9-1)*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

 (4)
> 

``


 

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