Summary

Fixes #712

This PR adds a clear error message when users attempt to use the iterator interface (init/step!) with Simple algorithms from SimpleNonlinearSolve.jl.

Problem

Previously, when users tried to use Simple algorithms with the iterator interface, they received a confusing error about a missing force_stop field. This made it unclear what the actual problem was.

Solution

Added an override of SciMLBase.init() for AbstractSimpleNonlinearSolveAlgorithm that throws a descriptive error message explaining:

• Simple algorithms don't support the iterator interface
• The iterator interface is only available for full-featured algorithms from NonlinearSolve.jl
• Users should either use algorithms like NewtonRaphson(), TrustRegion(), etc., or use solve(prob, alg) directly

Changes

• lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl: Added SciMLBase.init() override with clear error message (lines 127-148)
• lib/SimpleNonlinearSolve/test/core/iterator_interface_tests.jl: Added tests to verify error behavior using @test_throws pattern

Testing

The test file uses the @testitem macro with tags=[:core], which means it's automatically discovered and run by @run_package_tests in runtests.jl.

All Simple algorithms tested:

• ✅ SimpleNewtonRaphson
• ✅ SimpleBroyden
• ✅ SimpleTrustRegion
• ✅ SimpleDFSane
• ✅ SimpleKlement
• ✅ SimpleLimitedMemoryBroyden

Tests verify:

• Error is thrown when calling init(prob, alg) using @test_throws
• Error message contains helpful guidance (checked via err.value)
• solve(prob, alg) still works correctly

Example Error Message

julia> init(prob, SimpleNewtonRaphson())
ERROR: The Simple algorithms from SimpleNonlinearSolve.jl do not support the iterator interface (init/step!).

The iterator interface is only available for the full-featured algorithms from NonlinearSolve.jl.

If you need the iterator interface, please use one of the following algorithms instead:
- NewtonRaphson()
- TrustRegion()
- LevenbergMarquardt()
- And other algorithms from NonlinearSolve.jl

If you want to solve the problem directly, use `solve(prob, alg)` instead of `init(prob, alg)`.

Algorithm attempted: SimpleNewtonRaphson{Nothing}

Test Plan

Run the core tests:

julia --project=lib/SimpleNonlinearSolve -e 'using Pkg; Pkg.test(test_args=["GROUP=core"])'

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