Is there a good example showing that the effort of providing the Jacobian to either a non-linear solver, a time-stepping solver or an optimization solver does pay off in reducing the number of (non-linear, right-hand side or objective) function evaluations? Thx.
It won’t if automatic differentiation is around because that will generally be accurate enough. It’s not hard to show against finite differences though, take a very stiff equation and do something like
Rodas5(autodiff=false) (ROBER?) and you’ll see the difference (since Rodas methods require an accurate Jacobian)
Thanks. Will give its a look.