refactor: splitting up of NonlinearSolve #109

Job	Run time
test (1.10, ubuntu-latest, core)	14m 17s
test (1.10, ubuntu-latest, adjoint)	8m 16s
test (1.10, ubuntu-latest, alloc_check)	8m 27s
test (1.10, macos-latest, core)	14m 27s
test (1.10, macos-latest, adjoint)	5m 20s
test (1.10, macos-latest, alloc_check)	5m 43s
test (1.10, windows-latest, core)	16m 38s
test (1.10, windows-latest, adjoint)	11m 39s
test (1.10, windows-latest, alloc_check)	10m 1s
test (1, ubuntu-latest, core)	24m 53s
test (1, ubuntu-latest, adjoint)	15m 56s
test (1, ubuntu-latest, alloc_check)	15m 32s
test (1, macos-latest, core)	18m 30s
test (1, macos-latest, adjoint)	9m 50s
test (1, macos-latest, alloc_check)	10m 40s
test (1, windows-latest, core)	26m 7s
test (1, windows-latest, adjoint)	16m 48s
test (1, windows-latest, alloc_check)	16m 33s
	4h 9m 37s

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