MATLAB: Solve a complex differential Riccati equation numerically

Question

I want to solve a complex differential Riccati equation numerically. I used ODE45 and ODE15s but The solution has unstable oscillation.

How can I solve a differential Riccati equation with complex values?

For example:

d/dt y(t)=((-1+(0.5*cost)) (y(t)^2) )+1

Answer 1

It is my code for ODE:

y0=[-1i*sqrt(2)];

tspan = [t_curr-h t_curr];

M = [1];

%%% A=[0 -1+0.5*cos(t);

%%% 1 0]

par = [A(1,1);A(1,2);A(2,1);A(2,2)];

options = odeset('Mass',M,'RelTol',1e-6,'AbsTol',[1e-6]);

[T_LL,LL] = ode45(@tabe,tspan,y0,options,par);

%%%%%%%%%%%

function out = tabe(t,y,parameters)

a11=parameters(1);

a12=parameters(2);

a21=parameters(3);

a22=parameters(4);

out = [(-a12*(y(1)^2))+(-(a11-a22)*y(1))+a21];

end

%%%%%%%%%%%%%%%%%%%%%%%%%

It is the answer of ODE45: