refactor: splitting up of NonlinearSolve #115

Job	Run time
test (1.10, ubuntu-latest, core)	14m 25s
test (1.10, ubuntu-latest, adjoint)	8m 16s
test (1.10, ubuntu-latest, alloc_check)	8m 36s
test (1.10, macos-latest, core)	14m 31s
test (1.10, macos-latest, adjoint)	5m 59s
test (1.10, macos-latest, alloc_check)	7m 0s
test (1.10, windows-latest, core)	16m 34s
test (1.10, windows-latest, adjoint)	10m 46s
test (1.10, windows-latest, alloc_check)	9m 51s
test (1, ubuntu-latest, core)	25m 38s
test (1, ubuntu-latest, adjoint)	15m 26s
test (1, ubuntu-latest, alloc_check)	14m 46s
test (1, macos-latest, core)	18m 15s
test (1, macos-latest, adjoint)	11m 0s
test (1, macos-latest, alloc_check)	9m 47s
test (1, windows-latest, core)	26m 24s
test (1, windows-latest, adjoint)	17m 5s
test (1, windows-latest, alloc_check)	15m 55s
	4h 10m 14s

Provide feedback