MATLAB: Error :RelTol must be a positive scalar.

ode45phase portraitsreltol

options=odeset('RelTol','1e-3','AbsTol','1e-4');

I am trying to plot phase portraits for a non autonomous system. The code gives me the following error: Error using odearguments (line 126) RelTol must be a positive scalar.

Could you please help me to fix it?

Best Answer

      options=odeset('RelTol',1e-3,'AbsTol',1e-4);

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MATLAB: Changing a parameter in a differential equation

Hi Sean,

you can pass the value of epsilon into the ode function with

[tSol,YSol]=ode45(@(t,Y) quantumsystem(t,Y,epsilon),tRange,Y0);

and

function dYdt = quantumsystem(t,Y,epsilon);
    x=Y(1);
    y=Y(2);
    z=Y(3);
    gamma=1/2;
    c=1;
    dtheta=gamma*c/(t^2 + c^2);
    dxdt=(-1/epsilon)*y - dtheta*z; 
    dydt=(1/epsilon)*x;
    dzdt=dtheta*x;
    dYdt=[dxdt;dydt;dzdt];
end

Since ode45 picks the time increments, different values of epsilon may lead to different lengths of tSol and YSol, but the information is there. One of the easier ways to deal with that issue is to set up a for loop with different values of epsilion and use

plot(tSol,z)
hold on

inside the loop as you are doing, only without the color specification.

MATLAB: AbsTol, RelTol

The absolute tolerance of 1e-3 is meaningless, when the values are very small, e.g. 1.234e-27. Then the relative tolerance is more useful.

The precision of the result is IEEE-64bit double in every case, but the accuracy is influenced by the tolerances. The tolerances are used to limit the local discretization error: If the difference between a high-accuracy and low-accuracy integration is higher than one of the tolerances, the step size is reduced.

If the tolerance is too low, the large number of steps will increase the accumulated rounding errors, while for a to high tolerance the local discretization errors dominate the accuracy of the result.

Best Answer

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MATLAB: Changing a parameter in a differential equation

MATLAB: AbsTol, RelTol

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