refactor: splitting up of NonlinearSolve #105

Job	Run time
test (1.10, ubuntu-latest, core)	14m 33s
test (1.10, ubuntu-latest, adjoint)	8m 18s
test (1.10, ubuntu-latest, alloc_check)	8m 27s
test (1.10, macos-latest, core)	9m 26s
test (1.10, macos-latest, adjoint)	5m 16s
test (1.10, macos-latest, alloc_check)	5m 40s
test (1.10, windows-latest, core)	16m 28s
test (1.10, windows-latest, adjoint)	10m 22s
test (1.10, windows-latest, alloc_check)	10m 5s
test (1, ubuntu-latest, core)	22m 5s
test (1, ubuntu-latest, adjoint)	15m 27s
test (1, ubuntu-latest, alloc_check)	14m 41s
test (1, macos-latest, core)	5m 10s
test (1, macos-latest, adjoint)	5m 58s
test (1, macos-latest, alloc_check)	3m 46s
test (1, windows-latest, core)	21m 54s
test (1, windows-latest, adjoint)	16m 49s
test (1, windows-latest, alloc_check)	16m 49s
	3h 31m 14s

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