All I think is to get a sine wave function when plotting T vs A(1), but I didn't get any output. help me to modify this program

format long
a = 0;
b = 4;
h = 0.1
V =1E-5
I1 = 0.2;
I2 = 0.8;
o = 3E5;
tc = 30E-9;
tf = 230E-6;
a1 = 0.1;
a2 =0.1;
P1 = 0.2;
P2 =0.2;
k= 0.17;

A1(1) = 0;
A2(1) = 0;
G1(1) = ;
G2(1) = 0;
O(1) = 0;

n = (b-a)/h ;
t = a + (0:n)*h;

func1 = @(G1,A1,A2,O) (1/tc).*(G1- a1).*A1 +(k./tc).*A2.*cos(O);           
func3 = @(G2,A2,A1,O)  (1/tc).*(G2- a2).*A2 +(k./tc).*A1.*cos(O);            
func2 = @(G1)    (1/tf).*(P1 - G1.*(I1+1));
func4 = @(G2)   (1/tf).*(P2 - G2.*(I2+1));
func5 = @(A1,A2,O)   o - (k./tc).*((A1./A2) + (A2./A1)).*sin(O);
for i = 1:n
    k1 = func1(G1(i),A1(i),A2(i),O(i));
    l1 = feval(func2, G1(i));
    m1 = feval(func3, G2(i),A1(i),A2(i),O(i));
    n1 = feval(func4, G2(i));
    q1 = feval(func5,A1(i),A2(i),O(i));
    
    k2 = feval(func1, A2(i)+(m1/2)*h, A1(i)+(k1/2)*h,  G1(i)+(l1/2)*h,  O(i)+(q1/2)*h);
    l2 = feval(func2, G1(i)+(l1*h/2));
    m2 = feval(func3, A2(i)+(m1/2)*h, A1(i)+(k1/2)*h,  G2(i)+(n1/2)*h,  O(i)+(q1/2)*h);
    n2 = feval(func4, G2(i)+(n1/2)*h);
    q2 = feval(func5, A2(i)+(m1/2)*h, A1(i)+(k1/2)*h, O(i)+(q1/2)*h );
    
    k3 = feval(func1, A2(i)+(m2/2)*h, A1(i)+(k2/2)*h,  G1(i)+(l2/2)*h,  O(i)+(q2/2)*h);
    l3 = feval(func2, G1(i)+(l2*h/2));
    m3 = feval(func3, A2(i)+(m2/2)*h, A1(i)+(k2/2)*h,  G2(i)+(n2/2)*h,  O(i)+(q2/2)*h);
    n3 = feval(func4, G2(i)+(n2/2)*h);
    q3 = feval(func5, A2(i)+(m2/2)*h, A1(i)+(k2/2)*h, O(i)+(q2/2)*h );
    
    k4 = feval(func1, A2(i)+(m3*h), A1(i)+(k3*h),  G1(i)+(l3*h),  O(i)+(q3*h));
    l4 = feval(func2, G1(i)+(l3*h));
    m4 = feval(func3, A2(i)+(m3*h), A1(i)+(k3*h),  G2(i)+(n3*h),  O(i)+(q3*h));
    n4 = feval(func4, G2(i)+(n3*h));
    q4 = feval(func5, A2(i)+(m3*h), A1(i)+(k3*h), O(i)+(q3*h) );
    
    A1(i+1) = A1(i) + (h/6)*(k1+(2*(k2+k3))+k4);   
    G1(i+1) = G1(i) + (h/6)*(l1+(2*(l2+l3))+l4);
    A2(i+1) = A2(i) + (h/6)*(m1+(2*(m2+m3))+m4); 
    G2(i+1) = G2(i) + (h/6)*(n1+(2*(n2+n3))+n4); 
    O(i+1)  = O(i) + (h/6)*(q1+(2*(q2+q3))+q4); 
end
subplot 321
plot(t,A1)

subplot 322
plot(t,A2)

subplot 323
plot(t,G1)

subplot 324
plot(t,G1)

subplot 325
plot(t,O)

[Sam Chak]

Hi @SAHIL SAHOO

What does your code do? Can you provide a brief explanation?

If you want to plot a simple sine wave, that should be very direct, isn't it? Unless, it has something to do your code.

[SAHIL SAHOO]

hey sam,

thanks for reply,

and this program I suppose to solve the 5 couple oscillator and the ouput should be sinusoidal wave between A(1) vs t.

these are equations that have to be solve by the ODE method.

[dpb]

Have you verified the calculation of your functions at the origin?

>> i = 1
    k1 = func1(G1(i),A1(i),A2(i),O(i))
    l1 = feval(func2, G1(i))
    m1 = feval(func3, G2(i),A1(i),A2(i),O(i))
    n1 = feval(func4, G2(i))
    q1 = feval(func5,A1(i),A2(i),O(i))
i =
     1
k1 =
     0
l1 =
  869.5652
m1 =
     0
n1 =
  869.5652
q1 =
   NaN
>> 

shows your func5 returns NaN initially and since plot() doesn't show NaN values, only the origin 0 point will be plotted. Similar problems exist for the other functions as well and your integration grows without bounds for those two for which it doesn't return NaN.

Need to use the debugger and step through and see where your formulation went wrong...

BTW, you can simplify the coding -- there's no need to use feval here;, just use the anonymous function handles with the argument lists as you did in the very first call for k1 everywhere--not sure why you would have changed after that line for l1, m1, ...

k1 = func1(G1(i),A1(i),A2(i),O(i));
l1 = func2(G1(i));
m1 = func3(G2(i),A1(i),A2(i),O(i));
n1 = func4(G2(i));
q1 = func5(A1(i),A2(i),O(i));
...

Unless this is homework and required to write the integration explicitly as part of the assignment, would be easier to use the built-in ODE solvers in MATLAB.

Answer 1

[VBBV]

format short
a = 0;
b = 4;
h = 0.1;
V =1E-5;
I1 = 0.2;
I2 = 0.8;
o = 3.5;  % what is this variable ?
tc = 3.0; % 
tf = 2.3;  %
a1 = 0.1;
a2 =0.1;
P1 = 0.2;
P2 =0.2;
k= 0.17;

% initial conditions 
A1(1) = 0.7; 
A2(1) = 0.5;
G1(1) = 0.5;
G2(1) = 0.5;
O(1) = 10;

n = (b-a)/h ;
t = a + (0:n)*h;

func1 = @(G1,A1,A2,O) (1/tc).*(G1- a1).*A1 +(k./tc).*A2.*cos(O);           
func3 = @(G2,A2,A1,O)  (1/tc).*(G2- a2).*A2 +(k./tc).*A1.*cos(O);            
func2 = @(G1)    (1/tf).*(P1 - G1.*(I1+1));
func4 = @(G2)   (1/tf).*(P2 - G2.*(I2+1));
func5 = @(A1,A2,O)   O - (k./tc).*((A1./A2) + (A2./A1)).*sin(O);
for i = 1:n
    k1 = feval(func1,G1(i),A1(i),A2(i),O(i));
    l1 = feval(func2, G1(i));
    m1 = feval(func3, G2(i),A1(i),A2(i),O(i));
    n1 = feval(func4, G2(i));
    q1 = feval(func5,A1(i),A2(i),O(i));
    
    k2 = feval(func1, A2(i)+(m1/2)*h, A1(i)+(k1/2)*h,  G1(i)+(l1/2)*h,  O(i)+(q1/2)*h);
    l2 = feval(func2, G1(i)+(l1*h/2));
    m2 = feval(func3, A2(i)+(m1/2)*h, A1(i)+(k1/2)*h,  G2(i)+(n1/2)*h,  O(i)+(q1/2)*h);
    n2 = feval(func4, G2(i)+(n1/2)*h);
    q2 = feval(func5, A2(i)+(m1/2)*h, A1(i)+(k1/2)*h, O(i)+(q1/2)*h);
    
    k3 = feval(func1, A2(i)+(m2/2)*h, A1(i)+(k2/2)*h,  G1(i)+(l2/2)*h,  O(i)+(q2/2)*h);
    l3 = feval(func2, G1(i)+(l2*h/2));
    m3 = feval(func3, A2(i)+(m2/2)*h, A1(i)+(k2/2)*h,  G2(i)+(n2/2)*h,  O(i)+(q2/2)*h);
    n3 = feval(func4, G2(i)+(n2/2)*h);
    q3 = feval(func5, A2(i)+(m2/2)*h, A1(i)+(k2/2)*h, O(i)+(q2/2)*h );
    
    k4 = feval(func1, A2(i)+(m3*h), A1(i)+(k3*h),  G1(i)+(l3*h),  O(i)+(q3*h));
    l4 = feval(func2, G1(i)+(l3*h));
    m4 = feval(func3, A2(i)+(m3*h), A1(i)+(k3*h),  G2(i)+(n3*h),  O(i)+(q3*h));
    n4 = feval(func4, G2(i)+(n3*h));
    q4 = feval(func5, A2(i)+(m3*h), A1(i)+(k3*h), O(i)+(q3*h));
    
    A1(i+1) = A1(i) + (h/6)*(k1+(2*(k2+k3))+k4);   
    G1(i+1) = G1(i) + (h/6)*(l1+(2*(l2+l3))+l4);
    A2(i+1) = A2(i) + (h/6)*(m1+(2*(m2+m3))+m4); 
    G2(i+1) = G2(i) + (h/6)*(n1+(2*(n2+n3))+n4); 
    O(i+1)  = O(i) + (h/6)*(q1+(2*(q2+q3))+q4);
end
subplot 321
plot(t,A1)

subplot 322
plot(t,A2)

subplot 323
plot(t,G1)

subplot 324
plot(t,G1)

subplot 325
plot(t,O)

Set intial conditions in a suitable to get desired result.

[VBBV]

Check also using ode45 or similar builtin functions and varying input parameter values, for comparison purposes.

[SAHIL SAHOO]

"Unable to perform assignment because the left and right sides have a different number of elements.

Error in laser2 (line 54)

A1(i+1) = A1(i) + (h/6)*(k1+(2*(k2+k3))+k4); "

I'm having this problem when I change

func2 = @(G1) (1/tf).*(P1 - G1.*(A1.*A1+1));

func4 = @(G2) (1/tf).*(P2 - G2.*(A2.*A2+1));

why this is happening, let me know how to solve this one?