{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,30]],"date-time":"2026-05-30T01:02:35Z","timestamp":1780102955173,"version":"3.54.0"},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,2,12]],"date-time":"2025-02-12T00:00:00Z","timestamp":1739318400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,2,12]],"date-time":"2025-02-12T00:00:00Z","timestamp":1739318400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["PID2022-141385NB-I00"],"award-info":[{"award-number":["PID2022-141385NB-I00"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2025,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Singly-TASE operators for the numerical solution of stiff differential equations were proposed by Calvo et al. in J.Sci. Comput. 2023 to reduce the computational cost of Runge\u2013Kutta-TASE (RKTASE) methods when the involved linear systems are solved by some <jats:italic>LU<\/jats:italic> factorization. In this paper we propose a modification of these methods to improve the efficiency by considering different TASE operators for each stage of the Runge\u2013Kutta. We prove that the resulting RKTASE methods are equivalent to <jats:italic>W<\/jats:italic>-methods (Steihaug and Wolfbrandt, Mathematics of Computation,1979) and this allows us to obtain the order conditions of the proposed Modified Singly-RKTASE (MSRKTASE) methods through the theory developed for the <jats:italic>W<\/jats:italic>-methods. We construct new MSRKTASE methods of order two and three and demonstrate their effectiveness through numerical experiments on both linear and nonlinear stiff systems. The results show that the MSRKTASE schemes significantly enhance efficiency and accuracy compared to previous Singly-RKTASE (SRKTASE) schemes.<\/jats:p>","DOI":"10.1007\/s10915-025-02813-4","type":"journal-article","created":{"date-parts":[[2025,2,12]],"date-time":"2025-02-12T06:32:45Z","timestamp":1739341965000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Modified Singly-Runge\u2013Kutta-TASE Methods for the Numerical Solution of Stiff Differential Equations"],"prefix":"10.1007","volume":"103","author":[{"given":"M.","family":"Calvo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6120-4427","authenticated-orcid":false,"given":"J. I.","family":"Montijano","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L.","family":"R\u00e1ndez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,2,12]]},"reference":[{"key":"2813_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109847","volume":"424","author":"M Bassenne","year":"2021","unstructured":"Bassenne, M., Fu, L., Mani, A.: Time-accurate and highly-stable explicit operators for stiff differential equations. J. Comput. Phys. 424, 109847 (2021)","journal-title":"J. Comput. Phys."},{"key":"2813_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110316","volume":"436","author":"M Calvo","year":"2021","unstructured":"Calvo, M., Montijano, J.I., R\u00e1ndez, L.: A note on the stability of time-accurate and highly-stable explicit operators for stiff differential equations. J. Comput. Phys. 436, 110316 (2021)","journal-title":"J. Comput. Phys."},{"key":"2813_CR3","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1016\/j.apnum.2023.04.001","volume":"200","author":"L Aceto","year":"2024","unstructured":"Aceto, L., Conte, D., Pagano, G.: On a generalization of time-accurate and highly-stable explicit operators for stiff problems. Appl. Numer. Math. 200, 2\u201317 (2024)","journal-title":"Appl. Numer. Math."},{"key":"2813_CR4","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s10915-023-02232-3","volume":"96","author":"M Calvo","year":"2023","unstructured":"Calvo, M., Fu, L., Montijano, J.I., R\u00e1ndez, L.: Singly TASE operators for the numerical solution of stiff differential equations by explicit Runge-Kutta schemes. J. Sci. Comput. 96, 17 (2023)","journal-title":"J. Sci. Comput."},{"key":"2813_CR5","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1090\/S0025-5718-1979-0521273-8","volume":"33","author":"T Steihaug","year":"1979","unstructured":"Steihaug, T., Wolfbrandt, A.: An attempt to avoid exact Jacobian and nonlinear equations in the numerical solution of stiff differential equations. Math. Comput. 33, 521\u2013534 (1979)","journal-title":"Math. Comput."},{"key":"2813_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-024-02579-1","volume":"100","author":"D Conte","year":"2024","unstructured":"Conte, D., Gonzalez-Pinto, S., Hernandez-Abreu, D., Pagano, G.: On approximate matrix factorization and TASE $$W$$-methods for the time integration of parabolic partial differential equations. J. Sci. Comput. 100, 1\u201328 (2024)","journal-title":"J. Sci. Comput."},{"key":"2813_CR7","volume-title":"Solving Ordinary Differential Equations II","author":"G Wanner","year":"1996","unstructured":"Wanner, G., Hairer, E.: Solving Ordinary Differential Equations II. Springer, Berlin (1996)"},{"key":"2813_CR8","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1093\/comjnl\/5.4.329","volume":"5","author":"HH Rosenbrock","year":"1963","unstructured":"Rosenbrock, H.H.: Some general implicit processes for the numerical solution of differential equations. Comput. J. 5, 329\u2013330 (1963)","journal-title":"Comput. J."},{"key":"2813_CR9","unstructured":"Kennedy, C.A., Carpenter, M.H.: Diagonally implicit Runge-Kutta methods for ordinary differential equations: a review. NASA\/TM-2016-219173 NASA Langley Research Center, 1\u2013162 (2016)"},{"key":"2813_CR10","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.apnum.2019.07.008","volume":"146","author":"CA Kennedy","year":"2019","unstructured":"Kennedy, C.A., Carpenter, M.H.: Diagonally implicit Runge-Kutta methods for stiff ODEs. Appl. Numerical Math. 146, 221\u2013244 (2019)","journal-title":"Appl. Numerical Math."},{"key":"2813_CR11","first-page":"56","volume":"274","author":"S Gonz\u00e1lez-Pinto","year":"2016","unstructured":"Gonz\u00e1lez-Pinto, S., Hern\u00e1ndez-Abreu, D., P\u00e9rez-Rodr\u00edguez, S., Weiner, R.: A family of three-stage third order AMF-Wmethods for the time integration of advection diffusion reaction PDEs. Appl. Math. Comput. 274, 56\u2013584 (2016)","journal-title":"Appl. Math. Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-025-02813-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-025-02813-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-025-02813-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T00:38:49Z","timestamp":1743295129000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-025-02813-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,12]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["2813"],"URL":"https:\/\/doi.org\/10.1007\/s10915-025-02813-4","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,12]]},"assertion":[{"value":"3 July 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 November 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 January 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 February 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"3"}}