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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\u2013Kutta (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 <jats:italic>k<\/jats:italic>\u2013stage, <jats:italic>k<\/jats:italic>th\u2013order explicit RK schemes under the action of Singly TASE operators of the same order is carried out for <jats:inline-formula><jats:alternatives><jats:tex-math>$$k \\le 4$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>k<\/mml:mi>\n                    <mml:mo>\u2264<\/mml:mo>\n                    <mml:mn>4<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. For orders two, three and four, particular schemes that are nearly strongly A\u2013stable 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\u2013stage fourth\u2013order 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.<\/jats:p>","DOI":"10.1007\/s10915-023-02232-3","type":"journal-article","created":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T12:01:59Z","timestamp":1685016119000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Singly TASE Operators for the Numerical Solution of Stiff Differential Equations by Explicit Runge\u2013Kutta Schemes"],"prefix":"10.1007","volume":"96","author":[{"given":"Manuel","family":"Calvo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lin","family":"Fu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6120-4427","authenticated-orcid":false,"given":"Juan I.","family":"Montijano","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luis","family":"R\u00e1ndez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,5,25]]},"reference":[{"key":"2232_CR1","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1002\/zamm.19800601005","volume":"60","author":"PJ van der Houwen","year":"1980","unstructured":"van der Houwen, P.J., Sommeijer, B.P.: On the internal stability of explicit, m-stage Runge\u2013Kutta methods for large m values. 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