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Solving an equation in Matlab

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Dear, I'm trying to resolve this equation for my thesis project, u and v are the values that I try to calculate, the only parameter that change is the Tx and Ty, all the other parameters are constant. I appreciate any help
Screen Shot 2020-02-12 at 1.08.04 PM.png
tx = [0.1 0.5 0.12 0.14 0.22 0.1 0.12 0.29]
ty = [0.4 0.12 0.34 0.14 0.13 0.03 0.2 0.13]
Omega = 7.3E-5;
latitude = -12;
f0 = 2*Omega*sind(latitude);
r = 1./(2.*24.*3600)
Hm = 25
rho = 1.025e3
dvdt0 = -r.*v0 - f0.*u0 -ty./(rho.*Hm);
dudt0 = -r.*u0 + f0.*v0 + tx./(rho.*Hm);

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Accepted Answer

Star Strider
Star Strider on 12 Feb 2020
These have analytic solutions:
syms u(t) v(t) f taux tauy Hm rho R u0 v0
du = diff(u);
dv = diff(v);
DE = [du - f*v == taux/(Hm*rho) - R*u; dv - f*u == taux/(Hm*rho) - R*v]
Soln = dsolve(DE, u(0)==u0, v(0)==v0)
u_Soln = Soln.u;
v_Soln = Soln.v;
u_Soln = simplify(u_Soln, 'Steps',500)
v_Soln = simplify(v_Soln, 'Steps',500)
u_fcn = matlabFunction(u_Soln)
v_fcn = matlabFunction(v_Soln)
Note that ‘u_fcn’ and ‘v_fcn’ are anonymous functions you can use outside of the Symbolic Math Toolbox.

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Star Strider
Star Strider on 13 Feb 2020
That is what I coded, yes.
Sherlock Holmes
Sherlock Holmes on 13 Feb 2020
Thanks Star, you helping me a lot, now im going to try to make the dsolve works, in that way I can add more terms to try new solutions, again, thanks you so much for your time... best regards.
syms u(t) v(t) f taux tauy Hm rho R u0 v0
du = diff(u);
dv = diff(v);
DE = [du - f*v == taux/(Hm*rho) - R*u; dv + f*u == tauy/(Hm*rho) - R*v]
Soln = dsolve(DE, u(0)==u0, v(0)==v0)
u_Soln = Soln.u;
v_Soln = Soln.v;
u_Soln = simplify(u_Soln, 'Steps',500)
v_Soln = simplify(v_Soln, 'Steps',500)
u_fcn = matlabFunction(u_Soln)
v_fcn = matlabFunction(v_Soln)
Star Strider
Star Strider on 13 Feb 2020
As always, my pleasure!
I will help as I can.

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