Solve numerically a system of first-order differential equations

69 views (last 30 days)
Hello everyone,
I have the following set of coupled first-order differential equations:
where a, b, c, d, e, f, and g are some known parameters.
I was wondering which could be a good attempt to solve numerically this system of differential equations.
Any suggestion?

Accepted Answer

Star Strider
Star Strider on 31 Mar 2020
Create the function symbolically:
syms a b c d e f g t x(t) y(t) z(t) T Y
Dx = diff(x);
Dy = diff(y);
Dz = diff(z);
Eqn1 = a*Dx/z+Dy == b;
Eqn2 = Dx/z-a*Dy == c*sin(2*y);
Eqn3 = Dz == d*(e/z-(f+g*sin(2*y))*z);
Eqn1s = simplify(lhs(Eqn1) - rhs(Eqn1), 'Steps', 100);
Eqn2s = simplify(lhs(Eqn2) - rhs(Eqn2), 'Steps', 100);
Eqn3s = simplify(lhs(Eqn3) - rhs(Eqn3), 'Steps', 100);
[VF,Subs] = odeToVectorField(Eqn1s, Eqn2s, Eqn3s);
odefcn = matlabFunction(VF, 'Vars',{T Y a b c d e f g});
producing (lightly edited):
odefcn = @(T,Y,a,b,c,d,e,f,g)[(Y(3).*(a.*b+c.*sin(Y(2).*2.0)))./(a.^2+1.0);(b-a.*c.*sin(Y(2).*2.0))./(a.^2+1.0);-(d.*(-e+f.*Y(3).^2+g.*sin(Y(2).*2.0).*Y(3).^2))./Y(3)];
Then use the solver of your choice to integrate it.

Sign in to comment.

More Answers (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!