@article{Tiwari2025,
title = {Symplectic Newton–Cotes product Integration methods for fractional Hamiltonian systems},
author = {Shruti Tiwari},
journal = {Indian Journal of Mathematics},
volume = {67},
number = {1},
year = {2025},
pages = {39--60},
issn = {0019-5324},
keywords = {Fractional Hamiltonian systems; Caputo fractional derivatives; Symplectic integrators; Closed Newton–Cotes product integration; Sum-of-exponentials history compression.},
abstract = {This work presents a novel class of composite product-integration closed Newton--Cotes (CNC) integrators specifically designed for Hamiltonian systems governed by Caputo fractional derivatives of order $1 < \alpha < 2$. The proposed methodology establishes explicit full-history convolution weights while constructing a discrete variational principle within an extended phase space, ultimately yielding a symplectic mapping. Through rigorous analysis, we demonstrate global error bounds of $O(h^{2-\alpha})$ for CNC-2 and $O(h^{4-\alpha})$ for CNC-4 under conventional regularity assumptions. The linear stability characteristics are analyzed via the generating function of convolution weights, while long-term energy drift behavior is quantified. Additionally, efficient implementation strategies are developed that achieve $O(1)$ per-step computational complexity through systematic history truncation and sum-of-exponentials compression techniques. Comprehensive numerical experiments validate the theoretical predictions and demonstrate superior performance relative to existing fractional integrators.}
}