Solving a PDE Using Finite Difference Method

[kitz2]

Hi

The equation is:

$$\frac{dP}{dt}-A*\frac{{d}^2P}{dx^2}-B*\frac{dC}{dt}=0$$

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

 

[CFDFEAGURU]

This is not a partial differential equation (pde) it is a second order ordinary differential equation (ode). Are there any boundary or initail conditions that must be satisfied ?

 

[kitz2]

Boundary and inital conditions:

C=Co , t=0, 0<=x<=inf.
C=Cdf x-> inf , t >0
P=Po , t=0 0<=x<=inf.
P=Po t>0 x-> inf.
P=Pw x=0 t>0

 

[coomast]

This is not a partial differential equation (pde) it is a second order ordinary differential equation (ode). Are there any boundary or initail conditions that must be satisfied ?

It is a partial differential equation, both t and x are the independent variables and P the dependent function to find. C is a given function, but I don't see how to solve it. Certainly numerical ways should be possible but I can't help you on this.

coomast