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October 15, 2025Open Access

Hierarchical Differential Algebraic Closure Framework for the General N-Body Problem: A Comprehensive Symbolic-numeric Approach with Explicit Complexity Bounds

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This framework generalizes the hierarchical closure for n-body systems, highlighting conservation laws and complexity bounds.

The method achieves machine-precision accuracy while preserving fundamental conservation laws.
A systematic polynomialization transforms Newtonian equations into a multivariate polynomial system.
Parameterization enables tractability for symmetric configurations in small to moderate n-body problems.
Mathematical validations confirm correctness through rigorous derivations and numerical protocols.

liu et al. (2025) studied this question.

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