# integro-differential equation?

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PWini on 26 Jun 2016
Commented: bloodtalon on 16 Jun 2017
I have a problem which I will try to describe in details. Please try to help me, because the exam is coming :) The task is to find the solution of the differential equation as follows:
A*d2v/dt2+B*dv/dt+C*v-P(t)=0
P(t)=integral(fun(t,z)dz)
So I have the integral function implemented into the diff equation, where the integration is not by t-time but some different parameter in this case z-height.
I know, I am not so experienced programmer and MATLAB user but please give me some advice how to write the script. If you need some more info about the nature of that mysterious functions ask me.

Roger Stafford on 27 Jun 2016
You should solve this using one of the ‘ode’ numerical differential equation functions for a second order equation in the ordinary way, with the exception that the function P(t) must be computed using matlab’s ‘integral’ function, which in turn uses the ‘fun’ function as its integrand. That means it will probably take a considerably longer time for execution because of the repeated full integration times. (I assume you know the limits of integration in P.)
You will of course have to furnish the ‘ode’ function the initial values of v and dv/dt at the initial value of t.

PWini on 27 Jun 2016
Ok, So I calculated P(t) in time domain and the result is a vector of solutions for different time periods. Now how to implement that force into the differential equation formulation? Because for every solution of that diff equation I have a set of results in time domain, but the real problem is I don't know how to connect the each result of integration to that diff equation problem. In my opinion I should obtain the integration with time parameters (in some kind of symbolic function) then solve the diff equetion and substitute the time parameter.
Torsten on 27 Jun 2016
If you have a vector for P(t) at different time instances in advance (it seems P(t) does not depend on v in your case), take a look at the example "ODE with Time-Dependent Terms" under
to see how to deal with it.
Best wishes
Torsten.

Claudio Gelmi on 30 Jan 2017
Take a look at this MATLAB solver:
"IDSOLVER: A general purpose solver for nth-order integro-differential equations": http://dx.doi.org/10.1016/j.cpc.2013.09.008
Best wishes,
Claudio

#### 1 Comment

bloodtalon on 16 Jun 2017
Just a link like this isn't helping. Could you actually give some instructions on how to use it and/or some examples, preferably of the one in the question?