Help with two 1st order diff eq

Hi all,

I need help solving two first order differential equations.

dphi=(akd).*((exp(-(phi)))-(exp(psi)));
dpsi=(epp)-(exp(psi))-((ba).*(dphi));

epp ba and akd are defined. Phi and Psi are my variables, where dphi is the derivative with respect to t and dpsi is the derivative with respect to t. I tried perusing the help files but cannot get it to work. We were advised to use ode15s.

I tried making the equations into a vector field to put into the function but also struggled with this. Sidenote; dphi can be substituted in the dpsi equation.

Thanks.

[James Tursa]

Please post what you have tried so far and then we can give suggestions and comments on how to fix your code etc.

[James Bader]

%u=[-1,1;-1,1]; epp=(exp(1)); ba=.5; akd=1.5;

%Y(1)=phi, Y(2)=psi

syms phi(t) psi(t)

ode1= diff(phi) == (akd).*((exp(-(phi)))-(exp(psi))); ode2= diff(psi) == (epp)-(exp(psi))-((ba).*(akd).*((exp(-(phi)))-(exp(psi))));

[V]= odeToVectorField(ode1,ode2);

F=@(phi,psi,t)[V];

sol = ode15s(F,[0 20], [.1 .1]);

[James Bader]

Error using odearguments (line 113) Inputs must be floats, namely single or double.

Error in ode15s (line 150) odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in RSDFevolve (line 27) sol = ode15s(F,[0 20], [.1 .1]);

This is the error message I receive.

Answer 1

[Stephan]

Hi,

you missed to make a function handle from your vector field like shown here - psi(t) and phi(t) are still symbolic in your function handle, this is the problem you have.

Try:

syms phi(t) psi(t) epp akd ba
eqn1 = (akd).*((exp(-(phi)))-(exp(psi))) == diff(phi,t);
eqn2 = (epp)-(exp(psi))-((ba).*diff(phi,t)) == diff(psi,t);
eqn = [eqn1 eqn2];
eqn = subs(eqn,[epp ba akd], [exp(1), 5, 1.5]);
V = odeToVectorField(eqn);
M = matlabFunction(V, 'vars', {'t','Y'});
y0 = [0.1, 0.1];
tspan = [0 20];
[t,y] = ode15s(M, tspan, y0);
plot(t,y(:,1),t,y(:,2))

[James Bader]

Thanks! I see one issue was not making even my defined variables symbolic (bleh). Also that I wasn't quite defining these variables correctly in my equations.