refactor: splitting up of NonlinearSolve #117

Job	Run time
test (1.10, ubuntu-latest, core)	14m 8s
test (1.10, ubuntu-latest, adjoint)	8m 32s
test (1.10, ubuntu-latest, alloc_check)	8m 19s
test (1.10, macos-latest, core)	1s
test (1.10, macos-latest, adjoint)	1s
test (1.10, macos-latest, alloc_check)	1s
test (1.10, windows-latest, core)	16m 37s
test (1.10, windows-latest, adjoint)	10m 10s
test (1.10, windows-latest, alloc_check)	9m 53s
test (1, ubuntu-latest, core)	19m 17s
test (1, ubuntu-latest, adjoint)	15m 56s
test (1, ubuntu-latest, alloc_check)	14m 35s
test (1, macos-latest, core)	1s
test (1, macos-latest, adjoint)	1s
test (1, macos-latest, alloc_check)	1s
test (1, windows-latest, core)	19m 6s
test (1, windows-latest, adjoint)	17m 21s
test (1, windows-latest, alloc_check)	16m 13s
	2h 50m 13s

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