148200 20250114175434.0 doi 10.1016/j.apnum.2024.10.005 sideral 141686 ART-2025-141686 eng Clavero, Carmelo Universidad de Zaragoza (orcid)0000-0003-1263-1996 A priori and a posteriori error estimates for efficient numerical schemes for coupled systems of linear and nonlinear singularly perturbed initial-value problems 2025 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. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R info:eu-repo/grantAgreement/ES/MINECO/MTM2017-83490-P info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Kumar, Shashikant Kumar, Sunil 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 208 (2025), 123-147 Appl. numer. math. APPLIED NUMERICAL MATHEMATICS 0168-9274 2140446 http://zaguan.unizar.es/record/148200/files/texto_completo.pdf Versión publicada 2160904 http://zaguan.unizar.es/record/148200/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:148200 articulos driver 2025-01-14-15:49:22 ARTICLE