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To assess the effectiveness of post-step velocity rescaling in mitigating energy drift in explicit numerical integration of celestial systems.

August 12, 2026Open Access

Eliminating Energy Drift in Explicit Integration via Post-Step Velocity Rescaling: A 26-Year Mercury Orbit Benchmark

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Technical note evaluates a method to eliminate energy drift in celestial simulations, suggesting practical applications for numerical integrators.

To assess the effectiveness of post-step velocity rescaling in mitigating energy drift in explicit numerical integration of celestial systems.
Evaluated post-step velocity rescaling applied to the 4th-order Runge-Kutta (RK4) method.
Constrained the state vector to a target energy surface at each integration step.
Conducted a 26-year simulation benchmarking to analyze energy stability.
Achieved zero drift in orbital semi-major axis (delta_a = 0.00 m) over 26 years compared to 70.4 m drift in standard RK4, h = 3600 s.
Effectively halted systematic energy drift in celestial system simulations.
Provided a lightweight correction method for explicit integration without requiring step-size reduction.

Maksym Koresh (2026) studied this question.

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Technical note evaluates a method to eliminate energy drift in celestial simulations, suggesting practical applications for numerical integrators.