refactor: splitting up of NonlinearSolve #119

Job	Run time
downgrade (1.10, core)	5m 10s
downgrade (1.10, adjoint)	5m 11s
downgrade (1.10, alloc_check)	5m 9s
test (1.10, ubuntu-latest, core)	5m 10s
test (1.10, ubuntu-latest, adjoint)	5m 9s
test (1.10, ubuntu-latest, alloc_check)	5m 8s
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)	5m 1s
test (1.10, windows-latest, adjoint)	5m 2s
test (1.10, windows-latest, alloc_check)	5m 2s
test (1, ubuntu-latest, core)	5m 3s
test (1, ubuntu-latest, adjoint)	5m 10s
test (1, ubuntu-latest, alloc_check)	5m 9s
test (1, macos-latest, core)	1s
test (1, macos-latest, adjoint)	1s
test (1, macos-latest, alloc_check)	1s
test (1, windows-latest, core)	5m 3s
test (1, windows-latest, adjoint)	5m 3s
test (1, windows-latest, alloc_check)	5m 11s
	1h 16m 47s

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