{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:10:26Z","timestamp":1760235026314,"version":"build-2065373602"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.42274101"],"award-info":[{"award-number":["No.42274101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012476","name":"Fundamental Research Funds for Central Universities of the Central South University","doi-asserted-by":"publisher","award":["Nos.2022zzts0665"],"award-info":[{"award-number":["Nos.2022zzts0665"]}],"id":[{"id":"10.13039\/501100012476","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2025,11]]},"DOI":"10.1007\/s11075-024-01973-y","type":"journal-article","created":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T05:03:11Z","timestamp":1730437391000},"page":"921-935","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An efficient acceleration technique of implicit schemes for quasi-linear parabolic problems"],"prefix":"10.1007","volume":"100","author":[{"given":"Kejia","family":"Pan","sequence":"first","affiliation":[]},{"given":"Jiajia","family":"Xie","sequence":"additional","affiliation":[]},{"given":"Kang","family":"Fu","sequence":"additional","affiliation":[]},{"given":"Hongling","family":"Hu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,11,1]]},"reference":[{"key":"1973_CR1","volume-title":"Computational Fluid Dynamics","author":"JD Anderson","year":"1995","unstructured":"Anderson, J.D., Wendt, J.: Computational Fluid Dynamics. Springer, New York (1995)"},{"key":"1973_CR2","unstructured":"Forsythe, G.E., Wasow, W.R.: Finite-difference methods for partial differential equations. Applied Mathematics Series (1960)"},{"issue":"2","key":"1973_CR3","first-page":"831","volume":"183","author":"C Bi","year":"2006","unstructured":"Bi, C.: Mortar upwind finite volume element method for convection diffusion problems. Appl. Math. Comput. 183(2), 831\u2013841 (2006)","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"1973_CR4","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1093\/imanum\/20.2.281","volume":"20","author":"M Sardella","year":"2000","unstructured":"Sardella, M.: On a coupled finite element-finite volume method for convection-diffusion problems. IMA J. Numer. Anal. 20(2), 281\u2013301 (2000)","journal-title":"IMA J. Numer. Anal."},{"issue":"4","key":"1973_CR5","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1016\/0022-4073(95)00095-3","volume":"54","author":"M D\u2019amico","year":"1995","unstructured":"D\u2019amico, M.: A Newton-Raphson approach for nonlinear diffusion equations in radiation hydrodynamics. J. Quant. Spectrosc. Radiat. Transf. 54(4), 655\u2013669 (1995)","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"issue":"2","key":"1973_CR6","doi-asserted-by":"publisher","first-page":"743","DOI":"10.1016\/j.jcp.2003.10.036","volume":"195","author":"CC Ober","year":"2004","unstructured":"Ober, C.C., Shadid, J.N.: Studies on the accuracy of time-integration methods for the radiation-diffusion equations. J. Comput. Phys. 195(2), 743\u2013772 (2004)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"1973_CR7","doi-asserted-by":"publisher","first-page":"1332","DOI":"10.1016\/j.jcp.2007.05.034","volume":"226","author":"DA Knoll","year":"2007","unstructured":"Knoll, D.A., Lowrie, R.B., Morel, J.E.: Numerical analysis of time integration errors for nonequilibrium radiation diffusion. J. Comput. Phys. 226(2), 1332\u20131347 (2007)","journal-title":"J. Comput. Phys."},{"issue":"254","key":"1973_CR8","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1090\/S0025-5718-05-01800-4","volume":"75","author":"G Akrivis","year":"2006","unstructured":"Akrivis, G., Makridakis, C., Nochetto, R.: A posteriori error estimates for the Crank-Nicolson method for parabolic equations. Math. Comput. 75(254), 511\u2013531 (2006)","journal-title":"Math. Comput."},{"issue":"1","key":"1973_CR9","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1108\/HFF-10-2016-0403","volume":"28","author":"X Cui","year":"2018","unstructured":"Cui, X., Yuan, G., Shen, Z.: An efficient solving method for nonlinear convection diffusion equation. Int. J. Numer. Methods for Heat Fluid Flow 28(1), 173\u2013187 (2018)","journal-title":"Int. J. Numer. Methods for Heat Fluid Flow"},{"issue":"1","key":"1973_CR10","doi-asserted-by":"publisher","first-page":"1181","DOI":"10.1016\/j.jcp.2007.05.015","volume":"226","author":"GL Olson","year":"2007","unstructured":"Olson, G.L.: Efficient solution of multi-dimensional flux-limited nonequilibrium radiation diffusion coupled to material conduction with second-order time discretization. J. Comput. Phys. 226(1), 1181\u20131195 (2007)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"1973_CR11","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1002\/num.21988","volume":"32","author":"X Cui","year":"2016","unstructured":"Cui, X., Yuan, G., Yue, J.: Numerical analysis and iteration acceleration of a fully implicit scheme for nonlinear diffusion problem with second-order time evolution. Numer. Methods Partial Differ. Equ. 32(1), 121\u2013140 (2016)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"5","key":"1973_CR12","doi-asserted-by":"publisher","first-page":"777","DOI":"10.4208\/jcm.2007-m2020-0058","volume":"39","author":"X Cui","year":"2021","unstructured":"Cui, X., Yuan, G., Zhao, F.: Analysis on a numerical scheme with second-order time accuracy for nonlinear diffusion equations. J. Comput. Math. 39(5), 777 (2021)","journal-title":"J. Comput. Math."},{"key":"1973_CR13","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1016\/j.jcp.2017.02.063","volume":"338","author":"S Bolding","year":"2017","unstructured":"Bolding, S., Hansel, J., Edwards, J.D., Morel, J.E., Lowrie, R.B.: Second-order discretization in space and time for radiation-hydrodynamics. J. Comput. Phys. 338, 511\u2013526 (2017)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"1973_CR14","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1137\/0716039","volume":"16","author":"J Douglas Jr","year":"1979","unstructured":"Douglas, J., Jr., Dupont, T., Ewing, R.E.: Incomplete iteration for time-stepping a Galerkin method for a quasilinear parabolic problem. SIAM J. Numer. Anal. 16(3), 503\u2013522 (1979)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"1973_CR15","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s00211-006-0025-2","volume":"104","author":"C Chun","year":"2006","unstructured":"Chun, C.: Construction of Newton-like iteration methods for solving nonlinear equations. Numer. Math. 104(3), 297\u2013315 (2006)","journal-title":"Numer. Math."},{"key":"1973_CR16","unstructured":"Yuan, G., Hang, X.: Acceleration methods of nonlinear iteration for nonlinear parabolic equations. J. Comput. Math. 412\u2013424 (2006)"},{"issue":"4","key":"1973_CR17","doi-asserted-by":"publisher","first-page":"844","DOI":"10.4208\/cicp.310110.161010a","volume":"10","author":"J Yue","year":"2011","unstructured":"Yue, J., Yuan, G.: Picard-Newton iterative method with time step control for multimaterial non-equilibrium radiation diffusion problem. Commun. Comput. Phys. 10(4), 844\u2013866 (2011)","journal-title":"Commun. Comput. Phys."},{"issue":"2","key":"1973_CR18","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1137\/S1064827502407354","volume":"25","author":"KS Kang","year":"2003","unstructured":"Kang, K.S.: P1 nonconforming finite element multigrid method for radiation transport. SIAM J. Sci. Comput. 25(2), 369\u2013384 (2003)","journal-title":"SIAM J. Sci. Comput."},{"issue":"17","key":"1973_CR19","doi-asserted-by":"publisher","first-page":"1851","DOI":"10.1016\/j.jqsrt.2009.04.002","volume":"110","author":"A Doicu","year":"2009","unstructured":"Doicu, A., Trautmann, T.: Picard iteration methods for a spherical atmosphere. J. Quant. Spectrosc. Radiat. Transf. 110(17), 1851\u20131863 (2009)","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"1973_CR20","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.advwatres.2011.12.013","volume":"38","author":"P Lott","year":"2012","unstructured":"Lott, P., Walker, H., Woodward, C., Yang, U.: An accelerated Picard method for nonlinear systems related to variably saturated flow. Adv. Water. Resour. 38, 92\u2013101 (2012)","journal-title":"Adv. Water. Resour."},{"issue":"1","key":"1973_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10444-020-09756-4","volume":"46","author":"F Zhao","year":"2020","unstructured":"Zhao, F., Cui, X., Yuan, G.: Iterative acceleration methods with second-order time accuracy for nonlinear diffusion equations. Adv. Comput. Math. 46(1), 1\u201334 (2020)","journal-title":"Adv. Comput. Math."},{"key":"1973_CR22","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718898","volume-title":"Solving Nonlinear Equations with Newton\u2019s Method","author":"CT Kelley","year":"2003","unstructured":"Kelley, C.T.: Solving Nonlinear Equations with Newton\u2019s Method. SIAM, Philadelphia (2003)"},{"key":"1973_CR23","doi-asserted-by":"crossref","unstructured":"Hu, H., Chen, C., Pan, K.: Time-extrapolation algorithm (TEA) for linear parabolic problems. J. Comput. Math. 183\u2013194 (2014)","DOI":"10.4208\/jcm.1310-FE1"},{"key":"1973_CR24","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/j.aml.2016.09.003","volume":"64","author":"X Wang","year":"2017","unstructured":"Wang, X., Chen, C.: Matrix time-extrapolation algorithm for solving semilinear parabolic problems. Appl. Math. Lett. 64, 162\u2013169 (2017)","journal-title":"Appl. Math. Lett."},{"issue":"2","key":"1973_CR25","doi-asserted-by":"publisher","first-page":"501","DOI":"10.4208\/aamm.2015.m1281","volume":"9","author":"C Chen","year":"2017","unstructured":"Chen, C., Wang, X., Hu, H.: A high-efficient algorithm for parabolic problems with time-dependent coefficients. Adv. Appl. Math. Mech. 9(2), 501\u2013514 (2017)","journal-title":"Adv. Appl. Math. Mech."},{"issue":"2","key":"1973_CR26","doi-asserted-by":"publisher","first-page":"933","DOI":"10.1137\/120892465","volume":"52","author":"B Li","year":"2014","unstructured":"Li, B., Gao, H., Sun, W.: Unconditionally optimal error estimates of a Crank-Nicolson Galerkin method for the nonlinear thermistor equations. SIAM J. Numer. Anal. 52(2), 933\u2013954 (2014)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"1973_CR27","first-page":"20","volume":"37","author":"X Cui","year":"2015","unstructured":"Cui, X., Yue, J.: Property analysis and fast solution of nonlinear discrete schemes for conservative diffusion equations. Math. Numer. Sin. 37(3), 20 (2015)","journal-title":"Math. Numer. Sin."},{"issue":"2","key":"1973_CR28","first-page":"238","volume":"44","author":"X Zhang","year":"2021","unstructured":"Zhang, X., Jin, Y., Qiao, H., Li, C.: Crank-Nicolson-type difference scheme of the 2D Allen-Cahn equation. J. Appl. Math. 44(2), 238\u2013250 (2021)","journal-title":"J. Appl. Math."},{"issue":"1","key":"1973_CR29","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/S0377-0427(02)00734-3","volume":"151","author":"A Slavova","year":"2003","unstructured":"Slavova, A., Zecca, P.: CNN model for studying dynamics and travelling wave solutions of Fitzhugh-Nagumo equation. J. Comput. Appl. Math. 151(1), 13\u201324 (2003)","journal-title":"J. Comput. Appl. Math."},{"issue":"4","key":"1973_CR30","doi-asserted-by":"publisher","first-page":"1055","DOI":"10.1016\/j.camwa.2018.10.038","volume":"77","author":"H Zhou","year":"2019","unstructured":"Zhou, H., Sheng, Z., Yuan, G.: Physical-bound-preserving finite volume methods for the Nagumo equation on distorted meshes. Comput. Math. Appl. 77(4), 1055\u20131070 (2019)","journal-title":"Comput. Math. Appl."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01973-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-024-01973-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01973-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:26:48Z","timestamp":1760164008000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-024-01973-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,1]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["1973"],"URL":"https:\/\/doi.org\/10.1007\/s11075-024-01973-y","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2024,11,1]]},"assertion":[{"value":"24 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 October 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 November 2024","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":"Competing interests"}}]}}