refactor: splitting up of NonlinearSolve #103

Job	Run time
test (1.10, ubuntu-latest, core)	14m 13s
test (1.10, ubuntu-latest, adjoint)	8m 25s
test (1.10, ubuntu-latest, alloc_check)	8m 31s
test (1.10, macos-latest, core)	14m 54s
test (1.10, macos-latest, adjoint)	7m 21s
test (1.10, macos-latest, alloc_check)	5m 26s
test (1.10, windows-latest, core)	16m 6s
test (1.10, windows-latest, adjoint)	10m 23s
test (1.10, windows-latest, alloc_check)	9m 51s
test (1, ubuntu-latest, core)	24m 45s
test (1, ubuntu-latest, adjoint)	15m 25s
test (1, ubuntu-latest, alloc_check)	14m 49s
test (1, macos-latest, core)	20m 2s
test (1, macos-latest, adjoint)	10m 45s
test (1, macos-latest, alloc_check)	9m 20s
test (1, windows-latest, core)	27m 5s
test (1, windows-latest, adjoint)	16m 45s
test (1, windows-latest, alloc_check)	16m 11s
	4h 10m 17s

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