Integro differential equation with convolution
I have an integro differential equation that I need to solve numerically. The equation is of the form:
dX/dt = cX - X(b + q*dX/dt),
where q*dX/dt denotes the convolution between q and dX/dt.
If I want to solve this numerically using Matlab, there is a problem:
The left hand side and the right hand side of the equation contains dX/dt, and because it is a convolution on the right hand side, I cannot split it. I have tried using a Laplace transform but this doesn't work, because of the product.
Any ideas on how to solve this numerically? Please help...