Novel Mathematical Framework for Geometric Numerical Integration

This research explores advanced mathematical structures like post-Hopf algebroids and post-Lie-Rinehart algebras, linking them to geometric numerical integration. The connection suggests potential improvements in numerical methods for simulating physical systems, particularly those preserving geometric properties.

• •Applies abstract algebra concepts to numerical analysis.
• •Focuses on geometric numerical integration, preserving properties.
• •Explores potential for new and improved numerical methods.