refactor: splitting up of NonlinearSolve #112

Job	Run time
test (1.10, ubuntu-latest, core)	37s
test (1.10, ubuntu-latest, adjoint)	38s
test (1.10, ubuntu-latest, alloc_check)	37s
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)	31s
test (1.10, windows-latest, adjoint)	35s
test (1.10, windows-latest, alloc_check)	31s
test (1, ubuntu-latest, core)	29s
test (1, ubuntu-latest, adjoint)	30s
test (1, ubuntu-latest, alloc_check)	30s
test (1, macos-latest, core)	1s
test (1, macos-latest, adjoint)	1s
test (1, macos-latest, alloc_check)	1s
test (1, windows-latest, core)	28s
test (1, windows-latest, adjoint)	29s
test (1, windows-latest, alloc_check)	30s
	6m 31s

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