2024/03/13 by Gianmarco Gurioli, Weijie Wang, Gurioli, Gianmarco +3 · 1 citation
Engineering · Mathematics · #65L03 #65L05 #65L06 #65P10 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2403.08597
openalex publication_date 2024/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a class of high-order methods to numerically solve Functional Differential Equations with Piecewise Continuous Arguments (FDEPCAs) is discussed. The framework stems from the expansion of the vector field associated with the reference differential equation along the shifted and scaled Legendre polynomial orthonormal basis, working on a suitable extension of Hamiltonian Boundary Value Methods. Within the design of the methods, a proper generalization of the perturbation results coming from the field of ordinary differential equations is considered, with the aim of handling the case of FDEPCAs. The error analysis of the devised family of methods is performed, while a few numerical tests on Hamiltonian FDEPCAs are provided, to give evidence to the theoretical findings and show the effectiveness of the obtained resolution strategy.