# How to solve the following (integro-differential eq.)

1. Mar 17, 2009

### Hortensius

Hi all,

I'm struggeling with an equation of the following form:

$$\frac{\partial A\left(x,t\right)}{\partial t} = \int_{x_0}^{x_1} f\left(x,x',t\right)A\left(x',t\right) dx'$$

The problem is defined on the interval $$x_0 \leq x \leq x_1$$, where $$f\left(x,x',t\right)$$ is a known function. We have the initial condition $$A\left(x,0\right) = g\left(x\right)$$.

For my specific problem I found the qualitative behavior of the solution $$A\left(x,t\right)$$ by straightforward numerical integration. But I would like to be able to find analytic solutions... Any suggestions on how to proceed here?
Any help is very much appreciated!!

Last edited: Mar 17, 2009