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How to solve a class of integro-differential equations system?

Hi everyone

I'm trying to solve a particular physical problem that leads to a system of integro-differential equation that never I found neither solved. The system is described by two state variables z(t) and $\Phi_2(t)$ ; $\Phi_1$ , $\rho$, $\pi$, Mr, nF and R are known constants. In the convolution integral, the functions v(t-$\tau$) and f(z) are known; the last one is coupled with the solution of the first differential equation. The function j( $\tau$) is also a solution of other differential equation or can be written as linear combination of known functions.

I would like use the native functions of Mathematica to solve this system before to try an Euler or collocation method. If someone has experience in this kind of problems I would appreciate any suggestion and comments.

Regards Javier Navarro

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I think your problem is the initial condition z(0) = 0 which make dz/dt(0) blow up for any nonzero Phi1 and Phi2(0)=0

POSTED BY: Kay Herbert

Hello Kay. Thanks for your comment. No, the initial condition z(0)=0 is not a problem because initially the first derivative tends to infinity; that's compatible with the physical problem. The way I by-passed z(0)=0 is to consider z(0) ~ $10^{-15}$. Regards Javier

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POSTED BY: Daniel Lichtblau
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