168466 20260205155159.0 doi 10.1007/s10915-026-03184-0 sideral 147905 ART-2026-147905 eng Conte, Dajana General Runge–Kutta TASE Methods for Reaction–Diffusion Problems 2026 The class of Time Accurate and highly Stable Explicit Runge–Kutta (RK–TASE) methods has been introduced by Bassenne, Fu and Mani (J. Comput. Phys. 2021) and then extended by Calvo, Montijano and Rández (J. Comput. Phys. 2021), and Aceto, Conte and Pagano (Appl. Numer. Math. 2024), for the efficient solution of stiff initial value problems. With the aim of making RK–TASE methods suitable for the efficient solution of semi–discretized reaction–diffusion Partial Differential Equations (PDEs), in this work we exploit a general formulation of the schemes that allows to reduce both their computational cost and error constants, obtaining also good stability properties for such problems. In particular, a thorough study of the accuracy and stability properties leads to new RK–TASE methods up to order five that are more efficient than existing ones. Several experiments show that the new proposed RK–TASE methods are able to efficiently solve models of PDEs from applications that require integration over long time intervals. Furthermore, they show the better performance of the new RK–TASE compared to other numerical schemes from the scientific literature. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/MICINN/PID2022-141385NB-I00 info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Montijano, Juan Ignacio (orcid)0000-0001-6120-4427 Pagano, Giovanni Paternoster, Beatrice Rández, Luis Universidad de Zaragoza (orcid)0000-0002-4238-3228 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 106 (2026), 57 [32 pp.] J. sci. comput. Journal of Scientific Computing 0885-7474 1868676 http://zaguan.unizar.es/record/168466/files/texto_completo.pdf Versión publicada 1239443 http://zaguan.unizar.es/record/168466/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:168466 articulos driver 2026-02-05-14:37:08 ARTICLE