The structural method for Ordinary Differential Equations
Numerical Analysis
2025-08-05 v1 Numerical Analysis
Abstract
We design and analyse a new numerical method to solve ODE system based on the structural method. We compute approximations of solutions together with its derivatives up to order by solving an entire block corresponding to time steps. We build the physical relations that connect the function and derivative approximations at each time step by using the ODE and its derivatives, and develop the structural equations that establish linear relations between the function and its derivative over the whole block of times steps. The non-linear system is solved and provide very accurate approximations with nice spectral resolution properties.
Cite
@article{arxiv.2508.02440,
title = {The structural method for Ordinary Differential Equations},
author = {S. Clain and M. T. Malheiro and G. J. Machado and R. Costa},
journal= {arXiv preprint arXiv:2508.02440},
year = {2025}
}