000168466 001__ 168466 000168466 005__ 20260205155159.0 000168466 0247_ $$2doi$$a10.1007/s10915-026-03184-0 000168466 0248_ $$2sideral$$a147905 000168466 037__ $$aART-2026-147905 000168466 041__ $$aeng 000168466 100__ $$aConte, Dajana 000168466 245__ $$aGeneral Runge–Kutta TASE Methods for Reaction–Diffusion Problems 000168466 260__ $$c2026 000168466 5060_ $$aAccess copy available to the general public$$fUnrestricted 000168466 5203_ $$aThe 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. 000168466 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/PID2022-141385NB-I00 000168466 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es 000168466 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000168466 700__ $$0(orcid)0000-0001-6120-4427$$aMontijano, Juan Ignacio 000168466 700__ $$aPagano, Giovanni 000168466 700__ $$aPaternoster, Beatrice 000168466 700__ $$0(orcid)0000-0002-4238-3228$$aRández, Luis$$uUniversidad de Zaragoza 000168466 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000168466 773__ $$g106 (2026), 57 [32 pp.]$$pJ. sci. comput.$$tJournal of Scientific Computing$$x0885-7474 000168466 8564_ $$s1868676$$uhttps://zaguan.unizar.es/record/168466/files/texto_completo.pdf$$yVersión publicada 000168466 8564_ $$s1239443$$uhttps://zaguan.unizar.es/record/168466/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000168466 909CO $$ooai:zaguan.unizar.es:168466$$particulos$$pdriver 000168466 951__ $$a2026-02-05-14:37:08 000168466 980__ $$aARTICLE