Do the ODE functions from MATLAB (i.e. ODE23, ODE24) handle complex numbers properly?

For example, I want to integrate the equation dy/dt = sqrt(t) + y for 't' from -10 to 10 and for initial 'y' values of 1 and 2.

To do this, I would use:

]

[t,y] = ode45(@(t,y) sqrt(t)+y,-10:10,[1 2]);

Answer 1

[MathWorks Support Team]

The ODE solvers in MATLAB 5 (R12) and later releases properly handle complex valued systems.

When writing code, keep in mind the following:

The ' operator implements produces the conjugate transpose, while the .' operator performs a non-conjugate transpose. Improperly using one when you want the other will result in unexpected solutions.

For example:

M = rand(2)+rand(2)*i

 M =

    0.4451 + 0.8462i   0.4660 + 0.2026i

    0.9318 + 0.5252i   0.4186 + 0.6721i

M.'

 ans =

    0.4451 + 0.8462i   0.9318 + 0.5252i

    0.4660 + 0.2026i   0.4186 + 0.6721i

M'

 ans =

    0.4451 - 0.8462i   0.9318 - 0.5252i

    0.4660 - 0.2026i   0.4186 - 0.6721i