How to use matlabFunction to create a proper function for ode45?

I have used Matlab's symbolic toolbox to derive a set of equations for a system of ODEs. This required me to set all of my variables as being dependent on time (e.g. syms x1(t)) because I needed to take time derivatives during the derivation.

Now, if I run matlabFunction() on the resulting expressing, it outputs a function handle that depends only on t, but what I need is a function handle that depends on (t, [x1(t);....;xn(t)]) for use in ode45. How do I obtain this function handle dynamically?

Answer 1

[Star Strider]

This is actually more straightforward than it looks. You first have to call odeToVectorField to create the essential function construction and then use matlabFunction to create it as a function.

In the matlabFunction call, use the 'Vars' argument to return the variables-of-interest in the order you want them. (Normally, ‘t’ would not be included, but you can request it with 'Vars'.) This code also contains a tweak that retrieves the substituted variables from the odeToVectorField call and displays them in the legend of the integrated function.

Example —

syms t w y(t) Y
Dy = diff(y,t);
D2y = diff(y,t,2);
Eqn = D2y + 0.2*Dy - y - y^3 == 0.3*cos(w*t);
[DEs,DEsbs] = odeToVectorField(Eqn);                        % Request Substituted Variables
DEfcn = matlabFunction(DEs, 'Vars',[t,Y,w])                 % Use 'Vars' To Put Arguments In The Correct Order

w = 10;
tspan = linspace(0,5,250);
ic = [0; 0];
[tv,ys] = ode45(@(t,yv) DEfcn(t,yv,w), tspan, ic);

figure(1)
plot(tv, ys)
grid
lgndc = sym2cell(DEsbs);                                    % Get Substituted Variables
lgnds = regexp(sprintf('%s\n', lgndc{:}), '\n','split');    % Create Cell Array
legend(lgnds(1:end-1), 'Location','NW')                     % Display Legend

That should do what you want.