preparing symbolic ODE for ode45
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Consider the following symbolic ODE:
syms gamma(t)
C1 = 2.4
C2 = 3.1
ode = diff(gamma, t, 2) == C1 * sin(gamma) + C2 * cos(diff(gamma))
Now, I want to convert the above expression to the function odefun which I can use with ode45:
function res = odefun(t, gamma)
res = [gamma(2);
2.4*sin(gamma(1)) + 3.1*cos(gamma(2))]
end
Are there ways to automate (parts of) this process? The above ode is only a simple example to illustrate my problem. The ode I'm really trying to solve has way more terms with coefficients.
Thanks
采纳的回答
Try something like this —
syms gamma(t) T Y
C1 = 2.4
C2 = 3.1
ode = diff(gamma, t, 2) == C1 * sin(gamma) + C2 * cos(diff(gamma))
[VF,Subs] = odeToVectorField(ode)
odefun = matlabFunction(VF, 'Vars',{T,Y})
ic = [0 1];
tspan = [0 10];
[t,omega] = ode45(odefun, tspan, ic);
figure
plot(t, omega)
grid
legend(string(Subs), 'Location','best')
The constants do not have to be specified in the original equations. They can be included as parameters, so for example —
syms gamma(t) T Y C1 C2
ode = diff(gamma, t, 2) == C1 * sin(gamma) + C2 * cos(diff(gamma))
odefun = matlabFunction(VF, 'Vars',{T,Y, [C1,C2]})
ic = [0 1];
tspan = [0 10];
CV = rand(1,2)
[t,omega] = ode45(@(t,omega)odefun(t,omega,CV), tspan, ic);
Now they can be changed in the numeric code (for example in a loop or nested loops) without having to re-derive them each time in the original symbolic code.
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