refactor: splitting up of NonlinearSolve #107

Job	Run time
test (1.10, ubuntu-latest, core)	14m 23s
test (1.10, ubuntu-latest, adjoint)	8m 32s
test (1.10, ubuntu-latest, alloc_check)	8m 25s
test (1.10, macos-latest, core)	13m 54s
test (1.10, macos-latest, adjoint)	6m 31s
test (1.10, macos-latest, alloc_check)	7m 3s
test (1.10, windows-latest, core)	16m 20s
test (1.10, windows-latest, adjoint)	10m 37s
test (1.10, windows-latest, alloc_check)	10m 45s
test (1, ubuntu-latest, core)	24m 38s
test (1, ubuntu-latest, adjoint)	15m 21s
test (1, ubuntu-latest, alloc_check)	14m 31s
test (1, macos-latest, core)	19m 45s
test (1, macos-latest, adjoint)	10m 26s
test (1, macos-latest, alloc_check)	11m 42s
test (1, windows-latest, core)	26m 27s
test (1, windows-latest, adjoint)	17m 6s
test (1, windows-latest, alloc_check)	16m 34s
	4h 13m 0s

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