{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T22:38:56Z","timestamp":1775169536737,"version":"3.50.1"},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T00:00:00Z","timestamp":1617840000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T00:00:00Z","timestamp":1617840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11501514"],"award-info":[{"award-number":["11501514"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LY19A010026"],"award-info":[{"award-number":["LY19A010026"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010031","name":"Postdoctoral Research Foundation of China","doi-asserted-by":"publisher","award":["2018M642131"],"award-info":[{"award-number":["2018M642131"]}],"id":[{"id":"10.13039\/501100010031","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":[[2021,5]]},"DOI":"10.1007\/s10915-021-01474-3","type":"journal-article","created":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T11:03:49Z","timestamp":1617879829000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Convergence and Stability in Maximum Norms of Linearized Fourth-Order Conservative Compact Scheme for Benjamin\u2013Bona\u2013Mahony\u2013Burgers\u2019 Equation"],"prefix":"10.1007","volume":"87","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2742-2188","authenticated-orcid":false,"given":"Qifeng","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Lingling","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,4,8]]},"reference":[{"key":"1474_CR1","doi-asserted-by":"crossref","first-page":"1759","DOI":"10.1016\/j.cnsns.2009.08.003","volume":"15","author":"S Abbasbandy","year":"2010","unstructured":"Abbasbandy, S., Shirzadi, A.: The first integral method for modified Benjamin\u2013Bona\u2013Mahony equation. Commun. Nonlinear SCI 15, 1759\u20131764 (2010)","journal-title":"Commun. Nonlinear SCI"},{"key":"1474_CR2","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1016\/j.amc.2006.04.069","volume":"182","author":"T Achouri","year":"2006","unstructured":"Achouri, T., Khiari, N., Omrani, K.: On the convergence of difference schemes for the Benjamin\u2013Bona\u2013Mahony (BBM) equation. Appl. Math. Comput. 182, 999\u20131005 (2006)","journal-title":"Appl. Math. Comput."},{"key":"1474_CR3","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.amc.2005.01.056","volume":"171","author":"K Al-Khaled","year":"2005","unstructured":"Al-Khaled, K., Momani, S., Alawneh, A.: Approximate wave solutions for generalized Benjamin\u2013Bona\u2013Mahony\u2013Burgers equations. Appl. Math. Comput. 171, 281\u2013292 (2005)","journal-title":"Appl. Math. Comput."},{"key":"1474_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.apnum.2020.03.015","volume":"154","author":"S Arora","year":"2020","unstructured":"Arora, S., Jain, R., Kukreja, V.K.: Solution of Benjamin\u2013Bona\u2013Mahony\u2013Burgers equation using collocation method with quintic Hermite splines. Appl. Numer. Math. 154, 1\u201316 (2020)","journal-title":"Appl. Numer. Math."},{"key":"1474_CR5","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/s10915-015-0089-1","volume":"70","author":"D Baffet","year":"2017","unstructured":"Baffet, D., Hesthaven, J.S.: High-order accurate local schemes for fractional differential equations. J. Sci. Comput. 70, 355\u2013385 (2017)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"1474_CR6","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1137\/110830800","volume":"50","author":"W Bao","year":"2012","unstructured":"Bao, W., Cai, Y.: Uniform error estimates of finite difference methods for the nonlinear Schr\u00f6dinger equation with wave operator. SIAM J. Numer. Anal. 50(2), 492\u2013521 (2012)","journal-title":"SIAM J. Numer. Anal."},{"key":"1474_CR7","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1007\/s00211-019-01058-2","volume":"143","author":"W Bao","year":"2019","unstructured":"Bao, W., Carles, R., Su, C., Tang, Q.: Regularized numerical methods for the logarithmic Schr\u00f6dinger equation. Numer. Math. 143, 461\u2013487 (2019)","journal-title":"Numer. Math."},{"key":"1474_CR8","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1098\/rsta.1972.0032","volume":"272","author":"TB Benjamin","year":"1972","unstructured":"Benjamin, T.B., Bona, J.L., Mahony, J.J.: Model equations for long waves in nonlinear dispersive systems. Philos. Trans. R. Soc. Lond. Ser. A 272, 47\u201378 (1972)","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A"},{"key":"1474_CR9","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1515\/GMJ.2011.0044","volume":"18","author":"G Berikelashvili","year":"2011","unstructured":"Berikelashvili, G., Mirianashvili, M.: A one-parameter family of difference schemes for the regularized long-wave equation. Georgian Math. J. 18, 639\u2013667 (2011)","journal-title":"Georgian Math. J."},{"issue":"1","key":"1474_CR10","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1002\/num.21810","volume":"30","author":"G Berikelashvili","year":"2014","unstructured":"Berikelashvili, G., Mirianashvili, M.: On the convergence of difference schemes for generalized Benjamin\u2013Bona\u2013Mahony equation. Numer. Methods Part. Differ. Equ. 30(1), 301\u2013320 (2014)","journal-title":"Numer. Methods Part. Differ. Equ."},{"key":"1474_CR11","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s00211-017-0943-1","volume":"139","author":"C Besse","year":"2018","unstructured":"Besse, C., M\u00e9sognon-Gireau, B., Noble, P.: Artficial boundary conditions for the linearized Benjamin\u2013Bona\u2013Mahony equation. Numer. Math. 139, 281\u2013314 (2018)","journal-title":"Numer. Math."},{"key":"1474_CR12","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1016\/j.chaos.2016.03.034","volume":"89","author":"MS Bruz\u00f3n","year":"2016","unstructured":"Bruz\u00f3n, M.S., Garrido, T.M., de la Rosa, R.: Conservation laws and exact solutions of a generalized Benjamin\u2013Bona\u2013Mahony\u2013Burgers equation. Chaos Solut. Fract. 89, 578\u2013583 (2016)","journal-title":"Chaos Solut. Fract."},{"key":"1474_CR13","doi-asserted-by":"crossref","first-page":"1430","DOI":"10.1016\/j.amc.2009.05.068","volume":"217","author":"A Cesar","year":"2010","unstructured":"Cesar, A., G\u00f3mez, S., Alvaro, H.S., Bernardo, A.F.: New periodic and soliton solutions for the generalized BBM and Burgers-BBM equations. Appl. Math. Comput. 217, 1430\u20131434 (2010)","journal-title":"Appl. Math. Comput."},{"key":"1474_CR14","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/j.camwa.2014.05.019","volume":"68","author":"M Dehghan","year":"2014","unstructured":"Dehghan, M., Abbaszadeh, M., Mohebbi, A.: The numerical solution of nonlinear high dimensional generalized Benjamin\u2013Bona\u2013Mahony\u2013Burgers equation via the meshless method of radial basis functions. Comput. Math. Appl. 68, 212\u2013237 (2014)","journal-title":"Comput. Math. Appl."},{"key":"1474_CR15","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.cam.2015.03.012","volume":"286","author":"M Dehghan","year":"2015","unstructured":"Dehghan, M., Abbaszadeh, M., Mohebbi, A.: The use of interpolating element-free Galerkin technique for solving 2D generalized Benjamin\u2013Bona\u2013Mahony\u2013Burgers and regularized long-wave equations on non-rectangular domains with error estimate. J. Comput. Appl. Math. 286, 211\u2013231 (2015)","journal-title":"J. Comput. Appl. Math."},{"key":"1474_CR16","doi-asserted-by":"crossref","first-page":"2031","DOI":"10.1016\/j.chaos.2007.09.080","volume":"40","author":"PG Est\u00e9vez","year":"2009","unstructured":"Est\u00e9vez, P.G., Kuru, S., Negro, J., Nieto, L.M.: Travelling wave solutions of the generalized Benjamin\u2013Bona\u2013Mahony equation. Chaos Solut. Fract. 40, 2031\u20132040 (2009)","journal-title":"Chaos Solut. Fract."},{"key":"1474_CR17","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.physleta.2007.03.062","volume":"368","author":"A Fakhari","year":"2007","unstructured":"Fakhari, A., Domairry, G., Ebrahimpour, A.: Approximate explicit solutions of nonlinear BBMB equations by homotopy analysis method and comparison with the exact solution. Phys. Lett. A 368, 64\u201368 (2007)","journal-title":"Phys. Lett. A"},{"key":"1474_CR18","doi-asserted-by":"crossref","first-page":"1836","DOI":"10.1016\/j.apm.2008.03.005","volume":"33","author":"ZZ Ganji","year":"2009","unstructured":"Ganji, Z.Z., Ganji, D.D., Bararnia, H.: Approximate general and explicit solutions of nonlinear BBMB equations by Exp-Function method. Appl. Math. Model. 33, 1836\u20131841 (2009)","journal-title":"Appl. Math. Model."},{"key":"1474_CR19","volume-title":"Difference Methods for Partial Differential Equations","author":"BY Guo","year":"1988","unstructured":"Guo, B.Y.: Difference Methods for Partial Differential Equations. Science Press, Beijing (1988)"},{"key":"1474_CR20","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1007\/PL00005413","volume":"86","author":"BY Guo","year":"2000","unstructured":"Guo, B.Y., Shen, J.: Laguerre\u2013Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Numer. Math. 86, 635\u2013654 (2000)","journal-title":"Numer. Math."},{"issue":"6","key":"1474_CR21","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.1002\/num.20330","volume":"24","author":"T Kadri","year":"2008","unstructured":"Kadri, T., Khiari, N., Abidi, F., Omrani, K.: Methods for the numerical solution of the Benjamin\u2013Bona\u2013Mahony\u2013Burgers equation. Numer. Methods Part. Differ. Equ. 24(6), 1501\u20131516 (2008)","journal-title":"Numer. Methods Part. Differ. Equ."},{"issue":"3\u20134","key":"1474_CR22","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1080\/00036810008840852","volume":"75","author":"S Kinami","year":"2000","unstructured":"Kinami, S., Mei, M., Omata, S.: Convergence to diffusion waves of the solutions for Benjamin\u2013Bona\u2013Mahony\u2013Burgers equations. Appl. Anal. 75(3\u20134), 317\u2013340 (2000)","journal-title":"Appl. Anal."},{"key":"1474_CR23","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1016\/j.camwa.2020.03.016","volume":"80","author":"KH Kumar","year":"2020","unstructured":"Kumar, K.H., Jiwari, R.: Legendre wavelets based numerical algorithm for simulation of multidimensional Benjamin\u2013Bona\u2013Mahony\u2013Burgers and Sobolev equations. Comput. Math. Appl. 80, 417\u2013433 (2020)","journal-title":"Comput. Math. Appl."},{"key":"1474_CR24","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1007\/s10915-019-01039-5","volume":"81","author":"S Kundu","year":"2019","unstructured":"Kundu, S., Pani, A.K.: Global stabilization of BBM-Burgers\u2019 type equations by nonlinear boundary feedback control laws: theory and finite element error analysis. J. Sci. Comput. 81, 845\u2013880 (2019)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"1474_CR25","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1002\/num.22246","volume":"34","author":"S Kundu","year":"2018","unstructured":"Kundu, S., Pani, A.K., Khebchareon, M.: Asymptotic analysis and optimal error estimates for Benjamin\u2013Bona\u2013Mahony\u2013Burgers\u2019 type equations. Numer. Methods Part. Differ. Equ. 34(3), 1053\u20131092 (2018)","journal-title":"Numer. Methods Part. Differ. Equ."},{"key":"1474_CR26","doi-asserted-by":"crossref","unstructured":"Lannes, D.: The water waves problem: mathematical analysis and asymptotics. In: Mathematical Surveys and Monographs, Vol. 188. AMS (2013)","DOI":"10.1090\/surv\/188"},{"key":"1474_CR27","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.amc.2017.05.022","volume":"311","author":"C Li","year":"2017","unstructured":"Li, C.: Linearized difference schemes for a BBM equation with a fractional nonlocal viscous term. Appl. Math. Comput. 311, 240\u2013250 (2017)","journal-title":"Appl. Math. Comput."},{"key":"1474_CR28","doi-asserted-by":"publisher","unstructured":"Li, X., Xing, Y., Chou, C.: Optimal energy conserving and energy dissipative local discontinuous Galerkin methods for the Benjamin\u2013Bona\u2013Mahony equation. J. Sci. Comput. 83, (2020). https:\/\/doi.org\/10.1007\/s10915-020-01172-6","DOI":"10.1007\/s10915-020-01172-6"},{"key":"1474_CR29","doi-asserted-by":"crossref","first-page":"1607","DOI":"10.1007\/s10915-019-00991-6","volume":"80","author":"P Lyu","year":"2019","unstructured":"Lyu, P., Vong, S.: A high-order method with a temporal nonuniform mesh for a time-fractional Benjamin\u2013Bona\u2013Mahony equation. J. Sci. Comput. 80, 1607\u20131628 (2019)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"1474_CR30","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1002\/num.22441","volume":"36","author":"P Lyu","year":"2020","unstructured":"Lyu, P., Vong, S.: A nonuniform L2 formula of Caputo derivative and its application to a fractional Benjamin\u2013Bona\u2013Mahony-type equation with nonsmooth solutions. Numer. Methods Part. Differ. Equ. 36(3), 579\u2013600 (2020)","journal-title":"Numer. Methods Part. Differ. Equ."},{"key":"1474_CR31","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/S0362-546X(97)00674-3","volume":"33","author":"M Mei","year":"1998","unstructured":"Mei, M.: Large-time behavior of solution for generalized Benjamin\u2013Bona\u2013Mahony\u2013Burgers equations. Nonlinear Anal. 33, 699\u2013714 (1998)","journal-title":"Nonlinear Anal."},{"key":"1474_CR32","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1006\/jdeq.1999.3638","volume":"158","author":"M Mei","year":"1999","unstructured":"Mei, M.: $$L_q$$-Decay rates of solutions for Benjamin\u2013Bona\u2013Mahony\u2013Burgers equations. J. Differ. Equ. 158, 314\u2013340 (1999)","journal-title":"J. Differ. Equ."},{"key":"1474_CR33","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1007\/s40314-015-0272-x","volume":"36","author":"A Mohebbi","year":"2017","unstructured":"Mohebbi, A., Faraz, Z.: Solitary wave solution of nonlinear Benjamin\u2013Bona\u2013Mahony\u2013Burgers equation using a high-order difference scheme. Comput. Appl. Math. 36, 915\u2013927 (2017)","journal-title":"Comput. Appl. Math."},{"key":"1474_CR34","doi-asserted-by":"crossref","first-page":"2126","DOI":"10.1016\/j.camwa.2011.06.060","volume":"62","author":"MA Noor","year":"2011","unstructured":"Noor, M.A., Noor, K.I., Al-Said, A.E.A.: Some new solitonary solutions of the modified Benjamin\u2013Bona\u2013Mahony equation. Comput. Math. Appl. 62, 2126\u20132131 (2011)","journal-title":"Comput. Math. Appl."},{"key":"1474_CR35","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1016\/j.amc.2005.12.046","volume":"180","author":"K Omrani","year":"2006","unstructured":"Omrani, K.: The convergence of fully discrete Galerkin approximations for the Benjamin\u2013Bona\u2013Mahony (BBM) equation. Appl. Math. Comput. 180, 614\u2013621 (2006)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"1474_CR36","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1002\/num.20256","volume":"24","author":"K Omrani","year":"2008","unstructured":"Omrani, K., Ayadi, M.: Finite difference discretization of the Benjamin\u2013Bona\u2013Mahony\u2013Burgers equation. Numer. Methods Part. Differ. Equ. 24(1), 239\u2013248 (2008)","journal-title":"Numer. Methods Part. Differ. Equ."},{"key":"1474_CR37","doi-asserted-by":"crossref","first-page":"3042","DOI":"10.1016\/j.camwa.2017.07.046","volume":"74","author":"\u00d6 Oru\u00e7","year":"2017","unstructured":"Oru\u00e7, \u00d6.: A new algorithm based on Lucas polynomials for approximate solution of 1D and 2D nonlinear generalized Benjamin\u2013Bona\u2013Mahony\u2013Burgers equation. Comput. Math. Appl. 74, 3042\u20133057 (2017)","journal-title":"Comput. Math. Appl."},{"issue":"12","key":"1474_CR38","first-page":"1409","volume":"15","author":"R Prado","year":"2002","unstructured":"Prado, R., Zuazua, E.: Asymptotic expansion for the generalized Benjamin\u2013Bona\u2013Mahony\u2013Burger equation. Differ. Integr. Equ. 15(12), 1409\u20131434 (2002)","journal-title":"Differ. Integr. Equ."},{"key":"1474_CR39","doi-asserted-by":"publisher","unstructured":"Shen, X., Zhu, A.: A Crank\u2013Nicolson linear difference scheme for a BBM equation with a time fractional nonlocal viscous term. Adv. Differ. Equ. 355, (2018). https:\/\/doi.org\/10.1186\/s13662-018-1815-4","DOI":"10.1186\/s13662-018-1815-4"},{"key":"1474_CR40","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.enganabound.2016.08.006","volume":"72","author":"E Shivanian","year":"2016","unstructured":"Shivanian, E., Jafarabadi, A.: More accurate results for nonlinear generalized Benjamin\u2013Bona\u2013Mahony\u2013Burgers (GBBMB) problem through spectral meshless radial point interpolation (SMRPI). Eng. Anal. Bound. Elem. 72, 42\u201354 (2016)","journal-title":"Eng. Anal. Bound. Elem."},{"key":"1474_CR41","first-page":"824","volume":"35","author":"M Stanislavova","year":"2005","unstructured":"Stanislavova, M.: On the global attractor for the damped Benjamin\u2013Bona\u2013Mahony equation. Discrete Contin. Dyn. S-A 35, 824\u2013832 (2005)","journal-title":"Discrete Contin. Dyn. S-A"},{"issue":"6","key":"1474_CR42","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1080\/00207160.2014.927059","volume":"92","author":"H Sun","year":"2015","unstructured":"Sun, H., Sun, Z.-Z.: On two linearized difference schemes for Burgers\u2019 equation. Int. J. Comput. Math. 92(6), 1160\u20131179 (2015)","journal-title":"Int. J. Comput. Math."},{"issue":"6","key":"1474_CR43","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.1002\/num.20402","volume":"25","author":"Z-Z Sun","year":"2009","unstructured":"Sun, Z.-Z.: Compact difference schemes for heat equation with Neumann boundary conditions. Numer. Methods Part. Differ. Equ. 25(6), 1320\u20131341 (2009)","journal-title":"Numer. Methods Part. Differ. Equ."},{"key":"1474_CR44","volume-title":"Numerical Methods of Partial Differential Equations","author":"Z-Z Sun","year":"2012","unstructured":"Sun, Z.-Z.: Numerical Methods of Partial Differential Equations, 2nd edn. Science Press, Beijing (2012)","edition":"2"},{"key":"1474_CR45","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.physleta.2007.02.085","volume":"367","author":"H Tari","year":"2007","unstructured":"Tari, H., Ganji, D.D.: Approximate explicit solutions of nonlinear BBMB equations by He\u2019s methods and comparison with the exact solution. Phys. Lett. A 367, 95\u2013101 (2007)","journal-title":"Phys. Lett. A"},{"key":"1474_CR46","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.na.2014.04.013","volume":"105","author":"M Wang","year":"2014","unstructured":"Wang, M.: Long time dynamics for a damped Benjamin\u2013Bona\u2013Mahony equation in low regularity spaces. Nonlinear Anal. 105, 134\u2013144 (2014)","journal-title":"Nonlinear Anal."},{"key":"1474_CR47","doi-asserted-by":"crossref","first-page":"5763","DOI":"10.3934\/dcds.2016053","volume":"36","author":"M Wang","year":"2016","unstructured":"Wang, M.: Sharp global well-posedness of the BBM equation in $$L^p$$ type Sobolev spaces. Discrete Contin. Dyn. S-A 36, 5763\u20135788 (2016)","journal-title":"Discrete Contin. Dyn. S-A"},{"key":"1474_CR48","doi-asserted-by":"publisher","unstructured":"Wang, X.P., Zhang, Q., Sun, Z.-Z.: The pointwise error estimates of two energy-preserving fourth-order compact schemes for viscous Burgers\u2019 equation. Adv. Comput. Math. 47, 23 (2021). https:\/\/doi.org\/10.1007\/s10444-021-09848-9","DOI":"10.1007\/s10444-021-09848-9"},{"key":"1474_CR49","doi-asserted-by":"publisher","first-page":"106339","DOI":"10.1016\/j.aml.2020.106339","volume":"105","author":"YM Wang","year":"2020","unstructured":"Wang, Y.M.: A high-order linearized and compact difference method for the time-fractional Benjamin\u2013Bona\u2013Mahony equation. Appl. Math. Lett. 105, 106339 (2020). https:\/\/doi.org\/10.1016\/j.aml.2020.106339","journal-title":"Appl. Math. Lett."},{"key":"1474_CR50","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1007\/s00033-007-6136-5","volume":"59","author":"H Yin","year":"2008","unstructured":"Yin, H., Chen, S., Jin, J.: Convergence rate to traveling waves for generalized Benjamin\u2013Bona\u2013Mahony\u2013Burgers equations. Z. Angew. Math. Phys. 59, 969\u20131001 (2008)","journal-title":"Z. Angew. Math. Phys."},{"key":"1474_CR51","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.amc.2016.02.037","volume":"284","author":"M Zarebnia","year":"2016","unstructured":"Zarebnia, M., Parvaz, R.: On the numerical treatment and analysis of Benjamin\u2013Bona\u2013Mahony\u2013Burgers equation. Appl. Math. Comput. 284, 79\u201388 (2016)","journal-title":"Appl. Math. Comput."},{"key":"1474_CR52","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1016\/0362-546X(94)00252-D","volume":"25","author":"L Zhang","year":"1995","unstructured":"Zhang, L.: Decay of solutions of generalized Benjamin\u2013Bona\u2013Mahony\u2013Burger equations in $$n$$-space dimensions. Nonlinear Anal. Theory Methods Appl. 25, 1343\u20131396 (1995)","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"1474_CR53","doi-asserted-by":"crossref","first-page":"1790","DOI":"10.1002\/num.22504","volume":"36","author":"Q Zhang","year":"2020","unstructured":"Zhang, Q., Liu, L., Zhang, J.: The numerical analysis of two linearized difference schemes for the Benjamin\u2013Bona\u2013Mahony\u2013Burgers equation. Numer. Methods Part. Differ. Equ. 36, 1790\u20131810 (2020)","journal-title":"Numer. Methods Part. Differ. Equ."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01474-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-021-01474-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01474-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,1]],"date-time":"2023-11-01T20:55:54Z","timestamp":1698872154000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-021-01474-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,8]]},"references-count":53,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,5]]}},"alternative-id":["1474"],"URL":"https:\/\/doi.org\/10.1007\/s10915-021-01474-3","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,8]]},"assertion":[{"value":"14 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 February 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 April 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"59"}}