A variable step-size implementation of the hybrid Nyström method for integrating Hamiltonian and stiff differential systems

Date

2023-04-18

Advisors

Journal Title

Journal ISSN

ISSN

Volume Title

Publisher

Springer

Type

Article

Peer reviewed

Yes

Abstract

The approximate solution to second-order Hamiltonian and stiff differential systems is obtained using an efficient hybrid Nyström method (HNM) in this manuscript. The development of the method considers three hybrid points that are selected by optimizing the local truncation errors of the main formulas. The properties of the proposed HNM are studied. An embedding-like procedure is explored and run in variable step-size mode to improve the accuracy of the HNM. The numerical integration of some second-order Hamiltonian and stiff model problems, such as the well-known Vander Pol, Fermi-Pasta-Ulam, and Duffing problems, demonstrate the improved impact of our devised error estimation and control strategy. Finally, it is essential to note that the proposed technique is efficient in terms of computational cost and maximum global errors.

Description

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.

Keywords

Hybrid Nyström method, Hamiltonian and stiff differential systems, Variable stepsize formulation, Error estimation and control, Collocation method

Citation

Rufai, M.A., Tran, T. and Anastassi, Z.A. (2023) A variable step-size implementation of the hybrid Nyström method for integrating Hamiltonian and stiff differential systems. Computational and Applied Mathematics, 42, 156

Rights

Research Institute

Institute of Artificial Intelligence (IAI)