refactor: splitting up of NonlinearSolve #116

Job	Run time
test (1.10, ubuntu-latest, core)	12m 29s
test (1.10, ubuntu-latest, adjoint)	8m 17s
test (1.10, ubuntu-latest, alloc_check)	8m 35s
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)	12m 22s
test (1.10, windows-latest, adjoint)	10m 6s
test (1.10, windows-latest, alloc_check)	10m 12s
test (1, ubuntu-latest, core)	12m 28s
test (1, ubuntu-latest, adjoint)	12m 28s
test (1, ubuntu-latest, alloc_check)	12m 28s
test (1, macos-latest, core)	1s
test (1, macos-latest, adjoint)	1s
test (1, macos-latest, alloc_check)	1s
test (1, windows-latest, core)	12m 23s
test (1, windows-latest, adjoint)	12m 24s
test (1, windows-latest, alloc_check)	12m 22s
	2h 16m 40s

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