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

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Yaswanth Sai
Yaswanth Sai 2018-11-7
评论： Yaswanth Sai 2018-11-10
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.
  2 个评论
Steven Lord
Steven Lord 2018-11-7
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
Yaswanth Sai 2018-11-10
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.

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madhan ravi
madhan ravi 2018-11-7
编辑：madhan ravi 2018-11-7
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)
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