If I have heat equation with unknown source function and I want to solve it. Can I consider any another exact solution of heat equation and substitution it in my equation to find unknown source function then I search about solution of this equation after put the source function.
No you can't because the solution it depends on the source of function
You could consider to use a general source function, such as a polynomial or a Fourier series. In this case the function itself is fixed, but the coefficients can be defined later. But I suspect that this approach will be more difficult then solving the heat equation for a well defined (finite) source function.
I see in some papers wrote this statement in all numerical experiments:
(We choose f and an appropriate Dirichlet boundary condition so that the exact solution) That's mean: the source function unknown .
In some cases you need to generlaize your soultion so that it can work for different source functions. I think it can be done by using the general approch .
I meant construct a general source function ( not specific one) that can be used to study different cases. This generally done to study the problem experimentally.
Dear Hameeda Oda Al-Humedi
This kind of problems is called inverse source problems and it should be solved together i.e. the solution (temperature) and heat source. See my publication for more information.
Regards
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