convolution integral with dde

Hi guys, I am trying to solve this differential equation using dde. I have a problem with the integral term. In the code shown below, tau is the delay but I cannot just specify a constant value because it is also in the integral which goes from 0 to t. Does anywone know how to deal with it? Thank you!

%%

function sol = exer_3

sol = dde23(@exer3f,tau,[0; 0],[0, 10]);

figure

plot(sol.x,sol.y)

function v = exer3f(t,y,Z)

k = 125; m = 5; F = 1; w = 8;

c=@(t)exp(-t^2);

ylag = Z(:,1);

v = zeros(2,1);

v(1)=y(2);

v(2) = -(k*y(1) - F*cos(w*t) + integral(@(tau)c(tau).*ylag(1), 0, t,'ArrayValued',true))./m;

[Torsten]

You have an integro-differential eqution -- dde23 does not help in this case.

Try

http://cpc.cs.qub.ac.uk/summaries/AEQU_v1_0.html

Best wishes

Torsten.

[Angie]

Hi Torsten,

Thank you very much for your help! I had a look at the files. Unfortunately I could not use the idsolver for my case.

If i use the 2nd order diff eq below, then the integral term has a derivative inside and the idsolver did not work for this case.

Otherwise I can use the state-space below, so there would be no derivatives inside the integral. Still I could not figure out how to modify the idsolver to use the state-space.

[Torsten]

If you substitute

y = u'

you arrive at the integro-differential equation

y'(t) = F/m * cos(w*t) - k/m*u(0) - 1/m * integral_{0}^{t} y(s)*(c(t-s)+k) ds 

which has the required form.

[Satheesh oe]

Hi,

can i know why there is (+k) tem in the integral "(c(t-s)+k)".

Regards,

satheesh