On Slide 15 of Lec 11, the Jacobian is set to 0 when defining the ODE system.
The exact same ODE system is solved here in the GSL docs:
Ordinary Differential Equations — GSL 2.7 documentation (gnu.org), in which they do define a Jacobian.
Why can we just set the Jacobian to 0 for the Van der Pol oscillator equation
by Charley Xu -
Number of replies: 1
In reply to Charley Xu
Re: Why can we just set the Jacobian to 0 for the Van der Pol oscillator equation
by Ramses van Zon -
We can do this because the gsl_odeiv2_step_rk8pd step type does not use the Jacobian. The GSL documentation on https://www.gnu.org/software/gsl/doc/html/ode-initval.html#c.gsl_odeiv2_step_type tells you which step types use the Jacobian. As to why the GSL documentation includes the Jacobian in the example, my guess is, it is either a misunderstanding of the stepping algorithm they choose (i.e., a mistake), or they wanted to leave the possibility open to switch to a step type that does use the Jacobian.