is my program for solving differential equation is correct or not?

to solve this couple differential equation i wrote a program,

Z1....Z5 is y(1)...y(5), X1...X5 is y(6).......y(10) and Φ1.......Φ5 is y(11).....y(15)

hence I want to sovle another equation which is

Φ2 - Φ1 = y(16)

Φ3 - Φ2 = y(17)

Φ4 - Φ3 = y(18)

Φ5 - Φ4 = y(19)

Φ1 - Φ5 = y(20)

while solving these equation I didn't ge any fluctuation in the graph is my program correct or not?

clc

ti = 0; 
tf = 70E-9;
tspan=[ti tf];
tp =1E-12;
T = 2E3;
P = 0.05;
k = (0.62).*10^(0);
c = 3E8;
N = 3;
n = k*(c/N)*tp

a = 3;




f = @(t,y) [  
                                     (P - y(1) - ((2.*y(1) +1).*(((y(6)))^2)))./T; 
                                     (P - y(2) - ((2.*y(2) +1).*(((y(7)))^2)))./T;
                                     (P - y(3) - ((2.*y(3) +1).*(((y(8)))^2)))./T; 
                                     (P - y(4) - ((2.*y(4) +1).*(((y(9)))^2)))./T; 
                                     (P - y(5) - ((2.*y(5) +1).*(((y(10)))^2)))./T;

                               (y(1).*y(6)) - n.*(y(7).*sin(y(12) - y(11)) + y(10).*sin(y(15)- y(11)));
                               (y(2).*y(7)) - n.*(y(8).*sin(y(13) - y(12)) + y(6).*sin(y(11) - y(12)));
                               (y(3).*y(8)) - n.*(y(9).*sin(y(14) - y(13)) + y(7).*sin(y(12) - y(13)));
                               (y(4).*y(9)) - n.*(y(10).*sin(y(15) - y(14)) + y(8).*sin(y(13) - y(14)));
                               (y(5).*y(10)) - n.*(y(6).*sin(y(11) - y(15)) + y(9).*sin(y(14) - y(15)));

                   -a.*(y(1))+ n.*((y(7)./y(6)).*(cos(y(12) - y(11))) + (y(10)/y(6)).*(cos(y(15) - y(11))));
                   -a.*(y(2))+ n.*((y(8)./y(7)).*(cos(y(13) - y(12))) + (y(6)/y(7)).*(cos(y(11) - y(12))));
                   -a.*(y(3))+ n.*((y(9)./y(8)).*(cos(y(14) - y(13))) + (y(7)/y(8)).*(cos(y(12) - y(13))));
                   -a.*(y(4))+ n.*((y(10)./y(9)).*(cos(y(15) - y(14))) + (y(8)/y(9)).*(cos(y(13) -y(14))));
                   -a.*(y(5))+ n.*((y(6)./y(10)).*(cos(y(11) - y(15))) + (y(9)/y(10)).*(cos(y(14) - y(15))));
                  
                                          y(12) - y(11);
                                          y(13) - y(12);
                                          y(14) - y(13);
                                          y(15) - y(14);
                                          y(11) - y(15);
                                    
                                      ];


y0=[0; 0; 0; 0; 0; 0.6; 0.6; 0.6 ; 0.6; 0.6; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0]*10E-3;
[time,Y] = ode45(f,tspan./tp,y0);


plot(time,Y(:,16));
hold on
plot(time,Y(:,18));
plot(time,Y(:,17));
plot(time,Y(:,19));
plot(time,Y(:,20));
hold off

n = 0.5167

[Torsten]

1. What are X_0 and phi_0 ?
2. I don't see cos(phi_j+1 - phi_j), cos(phi_j - phi_j-1), sin(phi_j+1 - phi_j), sin(phi_j - phi_j-1) in your code.
3. y(16) - y(20) must be calculated after you get back y(1) - y(15) from ODE45. They are not part of the system of differential equations.

Maybe there are additional errors - I didn't check that rigorously.

[SAHIL SAHOO]

hello

I X1...X5 are the amplitude and i assing them from y(6)...y(10), and phi are the phase and i assing them y(11)...y(15).

I edited the code you can clearly see the cos(phi_j+1 - phi_j), cos(phi_j - phi_j-1), sin(phi_j+1 - phi_j), sin(phi_j - phi_j-1)

and your third point, I don't know how to do that please tell me.

thanks

[Torsten]

your third point, I don't know how to do that please tell me.

Remove y(16) up to y(20) from the function for the differential equation and use

hold on
plot(time,Y(:,12)-Y(:,11))
plot(time,Y(:,13)-Y(:,12))
plot(time,Y(:,14)-Y(:,13))
plot(time,Y(:,15)-Y(:,14))
plot(time,Y(:,11)-Y(:,15))
hold off

instead of

plot(time,Y(:,16));
hold on
plot(time,Y(:,18));
plot(time,Y(:,17));
plot(time,Y(:,19));
plot(time,Y(:,20));
hold off