000127026 001__ 127026
000127026 005__ 20230830121846.0
000127026 0247_ $$2doi$$a10.1007/s10915-023-02232-3
000127026 0248_ $$2sideral$$a134326
000127026 037__ $$aART-2023-134326
000127026 041__ $$aeng
000127026 100__ $$0(orcid)0000-0002-3312-5710$$aCalvo, Manuel$$uUniversidad de Zaragoza
000127026 245__ $$aSingly TASE Operators for the Numerical Solution of Stiff Differential Equations by Explicit Runge–Kutta Schemes
000127026 260__ $$c2023
000127026 5060_ $$aAccess copy available to the general public$$fUnrestricted
000127026 5203_ $$aIn this paper new explicit integrators for numerical solution of stiff evolution equations are proposed. As shown by Bassenne, Fu and Mani in (J Comput Phys 424:109847, 2021), the action on the original vector field of the stiff equations of an appropriate time-accurate and highly-stable explicit (TASE) linear operator, allows us to use explicit Runge–Kutta (RK) schemes with these modified equations so that the resulting algorithm becomes stable for the original stiff equations. Here a new family of TASE operators is considered. The new operators, called Singly TASE, have the advantage over the TASE operators of Bassenne et al. that the action on the vector field depends on the powers of the inverse of only one matrix, which can be computationally more simple, without loosing stability properties. A complete study of the linear stability properties of k–stage, kth–order explicit RK schemes under the action of Singly TASE operators of the same order is carried out for k≤4. For orders two, three and four, particular schemes that are nearly strongly A–stable and therefore suitable for stiff problems are devised. Further, explicit RK schemes with orders three and four that can be implemented with only two storage locations under the action of Singly TASE operators of the same order are discussed. A particular implementation of the classical four–stage fourth–order RK scheme with two Singly TASE operators is presented. A set of numerical experiments has been conducted to demonstrate the performance of the new schemes by comparing with previous RKTASE and other established methods. The main conclusion is that the new integrators provide a very simple solver for stiff systems with good stability properties and avoids the difficulties of using implicit algorithms.
000127026 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/PID2019-109045GB-C31
000127026 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000127026 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000127026 700__ $$aFu, Lin
000127026 700__ $$0(orcid)0000-0001-6120-4427$$aMontijano, Juan I.$$uUniversidad de Zaragoza
000127026 700__ $$0(orcid)0000-0002-4238-3228$$aRández, Luis$$uUniversidad de Zaragoza
000127026 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000127026 773__ $$g96, 1 (2023), 17 [24 pp.]$$pJ. sci. comput.$$tJournal of Scientific Computing$$x0885-7474
000127026 8564_ $$s1109467$$uhttps://zaguan.unizar.es/record/127026/files/texto_completo.pdf$$yVersión publicada
000127026 8564_ $$s1346044$$uhttps://zaguan.unizar.es/record/127026/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000127026 909CO $$ooai:zaguan.unizar.es:127026$$particulos$$pdriver
000127026 951__ $$a2023-08-30-09:58:51
000127026 980__ $$aARTICLE