refactor: splitting up of NonlinearSolve #111

Job	Run time
test (1.10, ubuntu-latest, core)	14m 40s
test (1.10, ubuntu-latest, adjoint)	8m 28s
test (1.10, ubuntu-latest, alloc_check)	8m 31s
test (1.10, macos-latest, core)	14m 33s
test (1.10, macos-latest, adjoint)	7m 19s
test (1.10, macos-latest, alloc_check)	6m 19s
test (1.10, windows-latest, core)	17m 31s
test (1.10, windows-latest, adjoint)	10m 15s
test (1.10, windows-latest, alloc_check)	10m 9s
test (1, ubuntu-latest, core)	25m 6s
test (1, ubuntu-latest, adjoint)	15m 12s
test (1, ubuntu-latest, alloc_check)	14m 37s
test (1, macos-latest, core)	19m 8s
test (1, macos-latest, adjoint)	9m 29s
test (1, macos-latest, alloc_check)	9m 33s
test (1, windows-latest, core)	27m 10s
test (1, windows-latest, adjoint)	17m 27s
test (1, windows-latest, alloc_check)	16m 43s
	4h 12m 10s

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