refactor: splitting up of NonlinearSolve #99

Job	Run time
test (min, ubuntu-latest, core)	25s
test (min, ubuntu-latest, adjoint)	27s
test (min, ubuntu-latest, alloc_check)	27s
test (min, macos-latest, core)	20s
test (min, macos-latest, adjoint)	21s
test (min, macos-latest, alloc_check)	34s
test (min, windows-latest, core)	47s
test (min, windows-latest, adjoint)	43s
test (min, windows-latest, alloc_check)	38s
test (1, ubuntu-latest, core)	48s
test (1, ubuntu-latest, adjoint)	57s
test (1, ubuntu-latest, alloc_check)	49s
test (1, macos-latest, core)	36s
test (1, macos-latest, adjoint)	51s
test (1, macos-latest, alloc_check)	52s
test (1, windows-latest, core)	1m 29s
test (1, windows-latest, adjoint)	1m 19s
test (1, windows-latest, alloc_check)	1m 21s
	13m 44s

Provide feedback