# how to solve 2nd order coupled system of differential equations with heaviside function using ode45 solver?

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Ronak Prateek on 22 Feb 2021
Commented: Ronak Prateek on 22 Feb 2021
i was trying to solve a system of coupled differential equations using ode45 solver with one of the equations having a heaviside function but i guess that it is assuming the value of zero of the heaviside function. please help.
syms P k1 k0 mw Izw b k22 mt Iyg kt dg ct Ixg v w kf delta;
P = 253;
k1 = 1.8;
k0 = 0.025;
mw = 2.53;
Izw = 0.0055;
b = 0.049;
k22 = 171;
mt = 0.41;
Iyg = 0.00013;
kt = 0.0045;
kf = 0.45;
delta = 0.009;
dg = 1.45/2;
ct = 0.00063;
Ixg = 0.00037;
v = 100;
w = 10.47*30;
couplode = @(t,y) [y(2); -((2*k22/v*(mt+mw))*y(2))+((2*k22/(mt+mw))*y(3))-((2*P*k1/(mt+mw))*y(1))-(kf*(y(1)+delta)*heaviside(y(1)-delta));y(4);(-2*(P*k0*b/(Izw+Iyg))*y(3))+((Ixg*w/(Izw+Iyg))*y(6));y(6);((-kt*dg^2/Iyg)*y(5))-((Ixg*w/Iyg)*y(4))-((ct*dg^2/Iyg)*y(6))];
[t,y] = ode45(couplode, [0 1000*pi], [0.001;0;0.314;0;0;0]);
figure(1)
plot(t, y)
hold on;
grid;
.pl

Star Strider on 22 Feb 2021
Numerical ODE solvers do not do well across non-differentiable discontinuities. The heaviside function in MATLAB is differentiable, so you likely can use it if you want.
I do not see where you have called heaviside or anything similar to it. What do you want to do?
Ronak Prateek on 22 Feb 2021
this is the system of equation which i was trying to solve with heaviside functions being highlighted below. my code displays the same result with or without the consideration of heaviside function terms. i believe the first highlighted term as shown below can be represented in the matlab by
(kf*(y(1)+delta)*heaviside(-y(1)-delta))
is it correct or not? please tell. sorry for not being clear.