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The equation is:

[tex]\frac{dP}{dt}-A*\frac{{d}^2P}{dx^2}-B*\frac{dC}{dt}=0[/tex]

dP/dt=A*d2P/dx^2 was solved using a finite difference method. If the function C(x,t) is known, is it possible to solve the whole equation by using the finite difference solution as a supplement to the complete solution. I mean solving dP/dt = B*dC/dt, and add them together or something. In case, how do I go about it?

Im using matlab and from the first finite difference solution I have an matrix for P(x,t) with all values for different x and t, and I also have a matrix for C(x,t) with all values for x and t. What I did was adding the P matrix with the C matrix multiplied with B , which have equal size. When the result was not as I wanted I tried adding the P matrix with P(matrix)+B*C(matrix), so I had 2*P(matrix) + B*C(matrix). Then I got a result which looked alright, but obviosuly it is just a shot in the dark, and not "math".

Im not very good at math as you might notice