refactor: splitting up of NonlinearSolve #125

Job	Run time
test (1.10, ubuntu-latest, core)	12m 45s
test (1.10, ubuntu-latest, adjoint)	8m 57s
test (1.10, ubuntu-latest, alloc_check)	8m 26s
downgrade (1.10, core)	13m 13s
test (1.10, macos-latest, core)	14m 2s
downgrade (1.10, adjoint)	8m 36s
downgrade (1.10, alloc_check)	8m 36s
test (1.10, macos-latest, adjoint)	6m 31s
test (1.10, macos-latest, alloc_check)	6m 1s
test (1.10, windows-latest, core)	14m 22s
test (1.10, windows-latest, adjoint)	10m 6s
test (1.10, windows-latest, alloc_check)	10m 4s
test (1, ubuntu-latest, core)	21m 24s
test (1, ubuntu-latest, adjoint)	16m 38s
test (1, ubuntu-latest, alloc_check)	15m 25s
test (1, macos-latest, core)	18m 17s
test (1, macos-latest, adjoint)	10m 30s
test (1, macos-latest, alloc_check)	11m 4s
test (1, windows-latest, core)	23m 31s
test (1, windows-latest, adjoint)	17m 47s
test (1, windows-latest, alloc_check)	16m 14s
	4h 32m 29s

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