now by defining several dimensionless variables, we got another form of diffusion equation:

X,T,U here are all dimensionless.

U with initial conditions:

and boundary conditions :

find the analytic solution of this problem.

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- Jan 19th 2009, 04:25 PMsilversandAnother form of diffusion equation
now by defining several dimensionless variables, we got another form of diffusion equation:

X,T,U here are all dimensionless.

U with initial conditions:

and boundary conditions :

find the analytic solution of this problem. - Jan 19th 2009, 04:26 PMsilversandwhat i got
what i got here,

but i have no idea how to solve. - Jan 19th 2009, 04:48 PMJester
If you were to solve

subject to

you would use a separation of variables and ultimately lead to

where

Since you have a source term in your new equation

then find a Fourier sine series for the source term of the form

and seek a solution of your porblem in the form

where is to be determined (this should give rise to an ODE for ). - Jan 19th 2009, 06:21 PMsilversandhow
how to determine the coefficients : ?

- Jan 20th 2009, 07:26 AMJester