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math.NA2025
Explicit invariant-preserving integration of differential equations using homogeneous projection
Benjamin Kwanen Tapley
We develop a general framework for numerically solving differential equations while preserving invariants. As in standard projection methods, we project an arbitrary base integrato…
math.NA2021
On the preservation of second integrals by Runge-Kutta methods
Benjamin K Tapley
One can elucidate integrability properties of ordinary differential equations (ODEs) by knowing the existence of second integrals (also known as weak integrals or Darboux polynomia…