Add nonlinear battery example to NonlinearProblem

[MarcBerliner]

This is an example nonlinear problem resulting from JuliaSimCompiler with 33 equations whose unknowns span ~13 orders of magnitude. The solution is quite sensitive to the algorithm choice and error tolerances. 15/20 of the tested algorithms failed to solve this problem (the solution L2-norm should be ~8e-7):

[Warn] Solver Newton Raphson (No line search) returned retcode Unstable with an residual norm = 292.3000724036127.
[Warn] Solver Newton Raphson (Hager & Zhang line search) returned retcode MaxIters with an residual norm = 274.02709301352945.
[Warn] Solver Newton Raphson (More & Thuente line search) returned retcode MaxIters with an residual norm = 272.9369057669025.
[Warn] Solver Newton Raphson (Nocedal & Wright line search) returned retcode MaxIters with an residual norm = 282.3447679256991.
[Warn] Solver Newton Trust Region returned retcode MaxIters with an residual norm = 87.55359385515213.
[Info] Solver Newton Trust Region (NLsolve radius update) successfully solved the problem.
[Warn] Solver Newton Trust Region (Nocedal Wright radius update) returned retcode MaxIters with an residual norm = 87.55359358466573.
[Warn] Solver Newton Trust Region (Hei radius update) returned retcode MaxIters with an residual norm = 87.72887154657568.
[Warn] Solver Newton Trust Region (Yuan radius update) returned retcode ConvergenceFailure with an residual norm = 292.3000724036127.
[Info] Solver Newton Trust Region (Bastin radius update) successfully solved the problem.
[Warn] Solver Newton Trust Region (Fan radius update) returned retcode MaxIters with an residual norm = 125.99151156402642.
[Info] Solver Levenberg-Marquardt (α_geodesic=0.75) successfully solved the problem.
[Warn] Solver Levenberg-Marquardt (α_geodesic, with CCholesky) returned retcode MaxIters with an residual norm = 0.0004065143786534784.
[Info] Solver Levenberg-Marquardt (α_geodesic=0.5) successfully solved the problem.
[Warn] Solver Levenberg-Marquardt (α_geodesic=0.5, with CCholesky) returned retcode MaxIters with an residual norm = 0.0004065143786534784.
[Warn] Solver Modified Powell (CMINPACK) threw an error: ErrorException("cfunction: closures are not supported on this platform").
[Warn] Solver Levenberg-Marquardt (CMINPACK) threw an error: ErrorException("cfunction: closures are not supported on this platform").
[Info] Solver Newton Raphson (NLSolveJL) successfully solved the problem.
[Warn] Solver Newton Trust Region (NLSolveJL) returned retcode Failure with an residual norm = 136.6473626403987.
[Warn] Solver Newton-Krylov (Sundials) had a residual of NaN.

cc @ChrisRackauckas

[avik-pal]

With the new release and some changes:

1. maxiters = 10000
2. termination_condition = AbsNormTerminationMode(). We are figuring out if we need to relax the current default here.
3. LM without the Normal Form has a subtle bug, which I will patch tomorrow

We are still the fastest here!

[MarcBerliner]

One suggestion on the above changes is that L2 errors > 1e-3 should not be considered converged. Can we do something to exclude those results?

[avik-pal]

I will create a PR with these changes. It seems MINPACK was returning converged even when it did not 🤷

[ChrisRackauckas]

Continuing with #792