@Markiyan HirnykThank You , this seems to be an interesting idea !

but , How can I get the Analytical function of the interpolant ?  (I need to multiply that with another function and then integrate it )

@Markiyan HirnykThank You , this seems to be an interesting idea !

but , How can I get the Analytical function of the interpolant ?  (I need to multiply that with another function and then integrate it )

@longrob  from 0 to about 1000 s

@longrob  from 0 to about 1000 s

Thank you,

I've tried this before, But, as you said, the taylor series does not resemble Q all over the interval of x, and therefore this method gives wrong results.

Thank you,

I've tried this before, But, as you said, the taylor series does not resemble Q all over the interval of x, and therefore this method gives wrong results.

Yes, this is heat equation and this Q came from another equation

( I'm Solving a Nonlinear heat transfer Equation by Homotopy Perturbation Method , after solving first equation this Q will appear in second equation)

I'm sure that's correct.

It is valid only for x from 0 to 0.03 and should increase as time increases.

Thank You

Yes, this is heat equation and this Q came from another equation

( I'm Solving a Nonlinear heat transfer Equation by Homotopy Perturbation Method , after solving first equation this Q will appear in second equation)

I'm sure that's correct.

It is valid only for x from 0 to 0.03 and should increase as time increases.

Thank You

@Markiyan Hirnyk  Yes , but the reason that I wanted to simplify this expression is to calculate that integral ! and I didn't notice any simplification in the last result

Thanks for your help ;)

@Markiyan Hirnyk  Yes , but the reason that I wanted to simplify this expression is to calculate that integral ! and I didn't notice any simplification in the last result

Thanks for your help ;)

Thanks for your reply

you are right, I fixed them  : W11(4).mw

but still simplify(Q,size)  gives a huge output ! and still can't calculate that integral ...

Thanks for your reply

you are right, I fixed them  : W11(4).mw

but still simplify(Q,size)  gives a huge output ! and still can't calculate that integral ...

Try this one please :

W11(2).mw

Try this one please :

W11(2).mw

Thank you Alex for your reply

Sorry, I'm new here ;)

this is my file : W11.mw

Q(x,t) is the Nonhomogenous part of a linear Partial Differential Equation, I want to solve it Analytically,

by "approximate" I mean, something like Pade approximaion of Q(x,t) , but I couln't find Pade approximation for two-variable functions.