Add IntervalArithmetic v0.23.0+ compatibility guide and robust examples

[ChrisRackauckas-Claude]

Summary

Adds comprehensive documentation and robust examples for IntervalArithmetic.jl v0.23.0+ compatibility, addressing breaking changes introduced in the latest version.

Problem Solved

IntervalArithmetic.jl v0.23.0 introduced breaking changes for IEEE 1788-2015 compliance that can cause failures in interval ODE examples:

❌ ArgumentError: `isfinite` is purposely not supported for intervals containing infinite bounds
❌ ArgumentError: `==` is purposely not supported for overlapping non-thin intervals  

Changes Made

📚 Documentation Updates

• Breaking changes guide for v0.23.0+ users
• Migration instructions from deprecated functions:
  • isfinite() → isbounded() for interval bounds checking
  • == → isequal_interval() for interval comparison
• Best practices for robust interval ODE solving

🛠️ Robust Example Code

Added solve_interval_ode_safely() function that:

• ✅ Handles solver failures gracefully with Euler fallback
• ✅ Checks interval bounds using isbounded()
• ✅ Uses fixed-step solvers to avoid adaptive step issues
• ✅ Provides clear error messages and fallback strategies

🧪 Testing Results

Verified with IntervalArithmetic v0.23.0:

• ✅ Original examples still work (with our π/3.0 fix)
• ✅ New robust examples handle edge cases gracefully
• ✅ All interval arithmetic operations function correctly
• ✅ Error handling provides useful fallback strategies

Benefits

🎯 User Experience: Clear guidance for v0.23.0+ users
🛡️ Robustness: Examples handle interval explosion gracefully
📖 Educational: Explains breaking changes and solutions
🔄 Backward Compatible: Works with both v0.22.x and v0.23.0+

Example Usage

The new robust solver automatically handles IntervalArithmetic v0.23.0 issues:

gaccel = interval(9.79, 9.81)
L = interval(0.99, 1.01) 
u₀ = [interval(0,0), interval(π/3.0 - 0.01, π/3.0 + 0.01)]
sol = solve_interval_ode_safely(gaccel, L, u₀, (0.0, 3.0))

This ensures the SciMLBook examples work reliably with the latest IntervalArithmetic.jl versions while providing educational value about handling numerical uncertainties.

🤖 Generated with Claude Code