How can I convert set of symbolic functions into function handle so that they can be used as input to ode45?

For example, I have to solve the following equations

if true
  syms x(t) y(t) z(t)
  eq1 = diff(x,t) == -x+3z;
  eq2 = diff(y,t) == -y+2z;
  eq3 = diff(z,t) == x^2-2z;
end

I can use ode45.

if true
  f = @(t,x) [-x(1)+3*x(3);-x(2)+2*x(3);x(1)^2-2*x(3)]; 
  [t,xa] = ode45(f,[0 1.5],[0 1/2 3]);
end

Is there any way I can generate the following line automatically from the equations I get(they are symbolic).

f = @(t,x) [-x(1)+3*x(3);-x(2)+2*x(3);x(1)^2-2*x(3)];

In my case, the equation is generated inside the code, so I don't know the coefficients beforehand to write that line.

[Steven Lord]

You could convert the symbolic expression into a MATLAB function as madhan ravi suggested, but have you tried the functionality included in Symbolic Math Toolbox to solve systems of differential equations directly?

[Yaswanth Sai]

I tried that, but there is no analytical solution to the equations I am trying to solve. So I will not be able to use the standard functionalities.

Answer 1

[madhan ravi]

EDITED

syms x(t) y(t) z(t)
eq1 = diff(x,t) == -x+3*z;
eq2 = diff(y,t) == -y+2*z;
eq3 = diff(z,t) == x^2-2*z;
vars = [x(t); y(t); z(t)]
V = odeToVectorField([eq1,eq2,eq3])
M = matlabFunction(V,'vars', {'t','Y'})

interval = [0 1.5];  %time interval
y0 = [0 1/2 3];      %initial conditions
ySol = ode45(M,interval,y0);
tValues = linspace(interval(1),interval(2),1000);
yValues = deval(ySol,tValues,1); %number 1 denotes first solution likewise you can mention 2 & 3 for the next two solutions
plot(tValues,yValues)

[Yaswanth Sai]

I tried using matlabFunction, but it was giving me warnings saying that in the above equations x, y and z are not valid matlab functions. When the equation has the terms x(t), y(t) and z(t), it is implicitly assuming that x, y, and z are functions.

If matlabFunction worked for you, can you put up some sample code to solve the above equations using ode45 if the initial equations are symbolic.

[Yaswanth Sai]

if true
  syms x(t) y(t) z(t)
end

After solving my problem I got the expressions

if true
  eq1 = diff(x,t) == -x+3z;
  eq2 = diff(y,t) == -y+2z;
  eq3 = diff(z,t) == x^2-2z;
end

The initial conditions are x(0) = 0, y(0) = 1/2, z(0) = 3 and the variable t belongs to [0,1.5].

I thought of using ode45 to solve the differential equations. For that purpose, I need to convert my symbolic equations into function handle.

[madhan ravi]

check edited answer

[Yaswanth Sai]

Thank you very much, Sir. I was stuck at this point for the last 2.5 hours.

[madhan ravi]

Anytime :) , glad to help