{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T16:51:45Z","timestamp":1758819105102},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T00:00:00Z","timestamp":1689552000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T00:00:00Z","timestamp":1689552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2024,3]]},"DOI":"10.1007\/s11075-023-01613-x","type":"journal-article","created":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T07:02:18Z","timestamp":1689577338000},"page":"1387-1412","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A stiff-cut splitting technique for stiff semi-linear systems of differential equations"],"prefix":"10.1007","volume":"95","author":[{"given":"Tao","family":"Sun","sequence":"first","affiliation":[]},{"given":"Hai-Wei","family":"Sun","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,7,17]]},"reference":[{"key":"1613_CR1","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1090\/S0025-5718-2012-02628-7","volume":"82","author":"G Akrivis","year":"2013","unstructured":"Akrivis, G.: Implicit-explicit multistep methods for nonlinear parabolic equations. Math. Comp. 82, 45\u201368 (2013)","journal-title":"Math. Comp."},{"key":"1613_CR2","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1007\/s002110050429","volume":"82","author":"G Akrivis","year":"1999","unstructured":"Akrivis, G., Crouzeix, M., Makridakis, C.: Implicit-explicit multistep methods for quasilinear parabolic equations. Numer. Math. 82, 521\u2013541 (1999)","journal-title":"Numer. Math."},{"key":"1613_CR3","doi-asserted-by":"publisher","first-page":"797","DOI":"10.1137\/0732037","volume":"32","author":"UM Ascher","year":"1995","unstructured":"Ascher, U.M., Ruuth, S.J., Wetton, B.T.R.: Implicit-explicit methods for time-dependent partial differential equations. SIAM J. Numer. Anal. 32, 797\u2013823 (1995)","journal-title":"SIAM J. Numer. Anal."},{"key":"1613_CR4","doi-asserted-by":"publisher","first-page":"1600","DOI":"10.1137\/060656929","volume":"45","author":"S Boscarino","year":"2007","unstructured":"Boscarino, S.: Error analysis of IMEX Runge-Kutta methods derived from differential-algebraic systems. SIAM J. Numer. Anal. 45, 1600\u20131621 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"1613_CR5","doi-asserted-by":"publisher","first-page":"1743","DOI":"10.1016\/j.jcp.2011.11.008","volume":"231","author":"C \u00c7elik","year":"2012","unstructured":"\u00c7elik, C., Duman, M.: Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative. J. Comput. Phys. 231, 1743\u20131750 (2012)","journal-title":"J. Comput. Phys."},{"key":"1613_CR6","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1007\/s10915-021-01431-0","volume":"87","author":"H Chen","year":"2021","unstructured":"Chen, H., Sun, H.W.: A dimensional splitting exponential time differencing scheme for multidimensional fractional Allen-Cahn equations. J. Sci. Comput. 87, 30 (2021)","journal-title":"J. Sci. Comput."},{"key":"1613_CR7","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1006\/jcph.2002.6995","volume":"176","author":"SM Cox","year":"2002","unstructured":"Cox, S.M., Matthews, P.C.: Exponential time differencing for stiff systems. J. Comput. Phys. 176, 430\u2013455 (2002)","journal-title":"J. Comput. Phys."},{"key":"1613_CR8","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/S0168-9274(97)00059-7","volume":"25","author":"J Frank","year":"1997","unstructured":"Frank, J., Hundsdorfer, W., Verwer, J.G.: On the stability of implicit-explicit linear multistep methods. Appl. Numer. Math. 25, 193\u2013205 (1997)","journal-title":"Appl. Numer. Math."},{"key":"1613_CR9","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.1137\/040611434","volume":"43","author":"M Hochbruck","year":"2005","unstructured":"Hochbruck, M., Ostermann, A.: Explicit exponential Runge-Kutta methods for semilinear parabolic problems. SIAM J. Numer. Anal. 43, 1069\u20131090 (2005)","journal-title":"SIAM J. Numer. Anal."},{"key":"1613_CR10","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s10915-022-01900-0","volume":"92","author":"X Huang","year":"2022","unstructured":"Huang, X., Li, D., Sun, H.W., Zhang, F.: Preconditioners with symmetrized techniques for space fractional Cahn-Hilliard equations. J. Sci. Comput. 92, 41 (2022)","journal-title":"J. Sci. Comput."},{"key":"1613_CR11","doi-asserted-by":"publisher","first-page":"565","DOI":"10.4208\/nmtma.OA-2022-0032","volume":"15","author":"X Huang","year":"2022","unstructured":"Huang, X., Lin, X.L., Ng, M.K., Sun, H.W.: Spectral analysis for preconditioning of multi-dimensional Riesz fractional diffusion equations. Numer. Math. Theory Methods Appl. 15, 565\u2013591 (2022)","journal-title":"Numer. Math. Theory Methods Appl."},{"key":"1613_CR12","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1016\/j.apnum.2021.07.003","volume":"169","author":"X Huang","year":"2021","unstructured":"Huang, X., Sun, H.W.: A preconditioner based on sine transform for two-dimensional semi-linear Riesz space fractional diffusion equations in convex domains. Appl. Numer. Math. 169, 289\u2013302 (2021)","journal-title":"Appl. Numer. Math."},{"key":"1613_CR13","doi-asserted-by":"publisher","first-page":"2016","DOI":"10.1016\/j.jcp.2007.03.003","volume":"225","author":"W Hundsdorfer","year":"2007","unstructured":"Hundsdorfer, W., Ruuth, S.J.: IMEX extensions of linear multistep methods with general monotonicity and boundedness properties. J. Comput. Phys. 225, 2016\u20132042 (2007)","journal-title":"J. Comput. Phys."},{"key":"1613_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2022.107047","volume":"118","author":"Y Kang","year":"2023","unstructured":"Kang, Y., Liao, H.L., Wang, J.: An energy stable linear BDF2 scheme with variable time-steps for the molecular beam epitaxial model without slope selection. Commun. Nonlinear Sci. Numer. Simul. 118, 107047 (2023)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"1613_CR15","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1016\/j.cam.2007.04.003","volume":"215","author":"T Koto","year":"2008","unstructured":"Koto, T.: IMEX Runge-Kutta schemes for reaction-diffusion equations. J. Comput. Appl. Math. 215, 182\u2013195 (2008)","journal-title":"J. Comput. Appl. Math."},{"key":"1613_CR16","volume-title":"Computational methods in ordinary differential equations","author":"JD Lambert","year":"1973","unstructured":"Lambert, J.D.: Computational methods in ordinary differential equations. John Wiley & Sons, London-New York-Sydney (1973)"},{"key":"1613_CR17","volume-title":"Numerical methods for ordinary differential systems","author":"JD Lambert","year":"1991","unstructured":"Lambert, J.D.: Numerical methods for ordinary differential systems. John Wiley & Sons Ltd, Chichester (1991)"},{"key":"1613_CR18","doi-asserted-by":"publisher","first-page":"2253","DOI":"10.1137\/21M1462398","volume":"60","author":"Z Li","year":"2022","unstructured":"Li, Z., Liao, H.L.: Stability of variable-step BDF2 and BDF3 methods. SIAM J. Numer. Anal. 60, 2253\u20132272 (2022)","journal-title":"SIAM J. Numer. Anal."},{"key":"1613_CR19","doi-asserted-by":"publisher","first-page":"795","DOI":"10.1007\/s11075-022-01342-7","volume":"92","author":"XL Lin","year":"2023","unstructured":"Lin, X.L., Huang, X., Ng, M.K., Sun, H.W.: A $$\\tau $$-preconditioner for a non-symmetric linear system arising from multi-dimensional Riemann-Liouville fractional diffusion equation. Numer. Algorithms 92, 795\u2013813 (2023)","journal-title":"Numer. Algorithms"},{"key":"1613_CR20","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.cam.2004.01.033","volume":"172","author":"MM Meerschaert","year":"2004","unstructured":"Meerschaert, M.M., Tadjeran, C.: Finite difference approximations for fractional advection-dispersion flow equations. J. Comput. Appl. Math. 172, 65\u201377 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"1613_CR21","doi-asserted-by":"publisher","first-page":"5238","DOI":"10.1016\/j.jcp.2008.01.050","volume":"227","author":"Q Nie","year":"2008","unstructured":"Nie, Q., Wan, F.Y.M., Zhang, Y., Liu, X.: Compact integration factor methods in high spatial dimensions. J. Comput. Phys. 227, 5238\u20135255 (2008)","journal-title":"J. Comput. Phys."},{"key":"1613_CR22","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1016\/j.jcp.2005.09.030","volume":"214","author":"Q Nie","year":"2006","unstructured":"Nie, Q., Zhang, Y., Zhao, R.: Efficient semi-implicit schemes for stiff systems. J. Comput. Phys. 214, 521\u2013537 (2006)","journal-title":"J. Comput. Phys."},{"key":"1613_CR23","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2474","author":"HH Qin","year":"2023","unstructured":"Qin, H.H., Pang, H.K., Sun, H.W.: Sine transform based preconditioning techniques for space fractional diffusion equations. Numer. Linear Algebr. Appl. (2023). https:\/\/doi.org\/10.1002\/nla.2474","journal-title":"Numer. Linear Algebr. Appl."},{"key":"1613_CR24","doi-asserted-by":"publisher","first-page":"2336","DOI":"10.1137\/16M1094324","volume":"55","author":"RR Rosales","year":"2017","unstructured":"Rosales, R.R., Seibold, B., Shirokoff, D., Zhou, D.: Unconditional stability for multistep ImEx schemes: theory. SIAM J. Numer. Anal. 55, 2336\u20132360 (2017)","journal-title":"SIAM J. Numer. Anal."},{"key":"1613_CR25","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s10543-006-0095-7","volume":"47","author":"V Savcenco","year":"2007","unstructured":"Savcenco, V., Hundsdorfer, W., Verwer, J.G.: A multirate time stepping strategy for stiff ordinary differential equations. BIT 47, 137\u2013155 (2007)","journal-title":"BIT"},{"key":"1613_CR26","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1016\/j.jcp.2018.09.044","volume":"376","author":"B Seibold","year":"2019","unstructured":"Seibold, B., Shirokoff, D., Zhou, D.: Unconditional stability for multistep ImEx schemes: practice. J. Comput. Phys. 376, 295\u2013321 (2019)","journal-title":"J. Comput. Phys."},{"key":"1613_CR27","doi-asserted-by":"publisher","first-page":"1703","DOI":"10.1090\/S0025-5718-2015-02917-2","volume":"84","author":"W Tian","year":"2015","unstructured":"Tian, W., Zhou, H., Deng, W.: A class of second order difference approximations for solving space fractional diffusion equations. Math. Comp. 84, 1703\u20131727 (2015)","journal-title":"Math. Comp."},{"key":"1613_CR28","doi-asserted-by":"publisher","first-page":"1824","DOI":"10.1137\/S1064827503429168","volume":"25","author":"JG Verwer","year":"2004","unstructured":"Verwer, J.G., Sommeijer, B.P.: An implicit-explicit Runge-Kutta-Chebyshev scheme for diffusion-reaction equations. SIAM J. Sci. Comput. 25, 1824\u20131835 (2004)","journal-title":"SIAM J. Sci. Comput."},{"key":"1613_CR29","first-page":"47","volume":"247","author":"A Xiao","year":"2014","unstructured":"Xiao, A., Zhang, G., Yi, X.: Two classes of implicit-explicit multistep methods for nonlinear stiff initial-value problems. Appl. Math. Comput. 247, 47\u201360 (2014)","journal-title":"Appl. Math. Comput."},{"key":"1613_CR30","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1007\/s12190-019-01291-w","volume":"62","author":"L Zhang","year":"2020","unstructured":"Zhang, L., Sun, H.W.: Numerical solution for multi-dimensional Riesz fractional nonlinear reaction-diffusion equation by exponential Runge-Kutta method. J. Appl. Math. Comput. 62, 449\u2013472 (2020)","journal-title":"J. Appl. Math. Comput."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-023-01613-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-023-01613-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-023-01613-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,15]],"date-time":"2024-02-15T21:30:45Z","timestamp":1708032645000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-023-01613-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,17]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["1613"],"URL":"https:\/\/doi.org\/10.1007\/s11075-023-01613-x","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,17]]},"assertion":[{"value":"18 April 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 June 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 July 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"The authors declare no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}