A priori and a posteriori error estimates for efficient numerical schemes for coupled systems of linear and nonlinear singularly perturbed initial-value problems

Clavero, Carmelo (Universidad de Zaragoza) ; Kumar, Shashikant ; Kumar, Sunil

Resumen: This work considers the numerical approximation of linear and nonlinear singularly perturbed initial value coupled systems of first-order, for which the diffusion parameters at each equation of the system are distinct and also they can have a different order of magnitude. To do that, we use two efficient discretization methods, which combine the backward differences and an appropriate splitting by components. Both a priori and a posteriori error estimates are proved for the proposed discretization methods. The developed numerical methods are more computationally efficient than those classical methods used to solve the same type of coupled systems. Extensive numerical experiments strongly confirm in practice the theoretical results and corroborate the superior performance of the current approach compared with previous existing approaches.

Idioma: Inglés

DOI: 10.1016/j.apnum.2024.10.005

Año: 2025

Publicado en: APPLIED NUMERICAL MATHEMATICS 208 (2025), 123-147
ISSN: 0168-9274

Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2017-83490-P

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)