{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T14:15:53Z","timestamp":1780496153263,"version":"3.54.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,8,20]],"date-time":"2024-08-20T00:00:00Z","timestamp":1724112000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,8,20]],"date-time":"2024-08-20T00:00:00Z","timestamp":1724112000000},"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":["Comp. Appl. Math."],"published-print":{"date-parts":[[2024,9]]},"DOI":"10.1007\/s40314-024-02883-4","type":"journal-article","created":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T06:06:48Z","timestamp":1724306808000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["A new robust compact difference scheme on graded meshes for the time-fractional nonlinear Kuramoto\u2013Sivashinsky equation"],"prefix":"10.1007","volume":"43","author":[{"given":"Jiawei","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoxuan","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuehua","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haixiang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,8,20]]},"reference":[{"issue":"6","key":"2883_CR1","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1063\/1.523009","volume":"17","author":"MJ Ablowitz","year":"1976","unstructured":"Ablowitz MJ, Ladik JF (1976) Nonlinear differential-difference equations and Fourier analysis. J Math Phys 17(6):1011\u20131018","journal-title":"J Math Phys"},{"key":"2883_CR2","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/BF01385769","volume":"59","author":"GD Akrivis","year":"1991","unstructured":"Akrivis GD, Dougalis VA, Karakashian OA (1991) On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schr\u00f6dinger equation. Numerische Mathematik 59:31\u201353","journal-title":"Numerische Mathematik"},{"key":"2883_CR3","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1016\/j.jcp.2014.09.031","volume":"280","author":"AA Alikhanov","year":"2015","unstructured":"Alikhanov AA (2015) A new difference scheme for the time fractional diffusion equation. J Comput Phys 280:424\u2013438","journal-title":"J Comput Phys"},{"issue":"6","key":"2883_CR4","doi-asserted-by":"publisher","first-page":"1254","DOI":"10.1080\/00207160.2020.1814262","volume":"98","author":"HP Bhatt","year":"2021","unstructured":"Bhatt HP, Chowdhury A (2021) A high-order implicit-explicit Runge-Kutta type scheme for the numerical solution of the Kuramoto-Sivashinsky equation. Int J Comput Math 98(6):1254\u20131273","journal-title":"Int J Comput Math"},{"key":"2883_CR5","doi-asserted-by":"publisher","first-page":"624","DOI":"10.1007\/s10915-018-0863-y","volume":"79","author":"H Chen","year":"2019","unstructured":"Chen H, Stynes M (2019) Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem. J Sci Comput 79:624\u2013647","journal-title":"J Sci Comput"},{"key":"2883_CR6","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.apnum.2021.05.022","volume":"169","author":"L Chen","year":"2021","unstructured":"Chen L, Lu S, Xu T (2021) Fourier spectral approximation for time fractional Burgers equation with nonsmooth solutions. Appl Numer Math 169:164\u2013178","journal-title":"Appl Numer Math"},{"issue":"2","key":"2883_CR7","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/s40096-021-00402-8","volume":"15","author":"O Ersoy Hepson","year":"2021","unstructured":"Ersoy Hepson O (2021) Numerical simulations of Kuramoto-Sivashinsky equation in reaction-diffusion via Galerkin method. Math Sci 15(2):199\u2013206","journal-title":"Math Sci"},{"key":"2883_CR8","doi-asserted-by":"crossref","unstructured":"Han XL, Guo TAO, Nikan O, Avazzadeh Z (2023) Robust implicit difference approach for the time-fractional Kuramoto-Sivashinsky equation with the non-smooth solution. Fractals 2340061","DOI":"10.1142\/S0218348X23400613"},{"key":"2883_CR9","doi-asserted-by":"publisher","first-page":"1749","DOI":"10.1007\/s11075-020-01036-y","volume":"87","author":"C Huang","year":"2021","unstructured":"Huang C, Stynes M (2021) $$\\alpha $$-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation. Numer Algor 87:1749\u20131766","journal-title":"Numer Algor"},{"issue":"2","key":"2883_CR10","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/s10915-022-01810-1","volume":"91","author":"C Huang","year":"2022","unstructured":"Huang C, Stynes M (2022) A sharp $$\\alpha $$-robust $$L^{\\infty }(H^1)$$ error bound for a time-fractional Allen-Cahn problem discretised by the Alikhanov $$L2-1_{\\sigma }$$ scheme and a standard FEM. J Sci Comput 91(2):43","journal-title":"J Sci Comput"},{"key":"2883_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2020.113334","volume":"389","author":"C Huang","year":"2021","unstructured":"Huang C, Stynes M, Chen H (2021) An $$\\alpha $$-robust finite element method for a multi-term time-fractional diffusion problem. J Comput Appl Math 389:113334","journal-title":"J Comput Appl Math"},{"issue":"2","key":"2883_CR12","first-page":"488","volume":"180","author":"H Jafari","year":"2006","unstructured":"Jafari H, Daftardar-Gejji V (2006) Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition. Appl Math Comput 180(2):488\u2013497","journal-title":"Appl Math Comput"},{"issue":"2","key":"2883_CR13","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1143\/PTP.55.356","volume":"55","author":"Y Kuramoto","year":"1976","unstructured":"Kuramoto Y, Tsuzuki T (1976) Persistent propagation of concentration waves in dissipative media far from thermal equilibrium. Prog Theor Phys 55(2):356\u2013369","journal-title":"Prog Theor Phys"},{"issue":"2","key":"2883_CR14","doi-asserted-by":"publisher","first-page":"567","DOI":"10.4208\/cicp.OA-2020-0124","volume":"30","author":"HL Liao","year":"2021","unstructured":"Liao HL, McLean W, Zhang J (2021) A second-order scheme with nonuniform time steps for a linear reaction-subdiffusion problem. Commun Comput Phys 30(2):567\u2013601","journal-title":"Commun Comput Phys"},{"key":"2883_CR15","unstructured":"Podlubny I (1999) Fractional differential equations, volume 198 of mathematics in science and engineering, pp 7\u201335"},{"key":"2883_CR16","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1016\/j.matcom.2019.05.017","volume":"166","author":"W Qiu","year":"2019","unstructured":"Qiu W, Chen H, Zheng X (2019) An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equations. Math Comput Simul 166:298\u2013314","journal-title":"Math Comput Simul"},{"key":"2883_CR17","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1016\/j.physa.2015.04.018","volume":"434","author":"S Sahoo","year":"2015","unstructured":"Sahoo S, Ray SS (2015) New approach to find exact solutions of time-fractional Kuramoto-Sivashinsky equation. Physica A Stat Mech Appl 434:240\u2013245","journal-title":"Physica A Stat Mech Appl"},{"issue":"1","key":"2883_CR18","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1146\/annurev.fl.15.010183.001143","volume":"15","author":"GI Sivashinsky","year":"1983","unstructured":"Sivashinsky GI (1983) Instabilities, pattern formation, and turbulence in flames. Annu Rev Fluid Mech 15(1):179\u2013199","journal-title":"Annu Rev Fluid Mech"},{"issue":"631\u2013653","key":"2883_CR19","first-page":"5116","volume":"225","author":"N Sugimoto","year":"1991","unstructured":"Sugimoto N (1991) Burgers equation with a fractional derivative; hereditary effects on nonlinear acoustic waves. J Fluid Mech 225(631\u2013653):5116","journal-title":"J Fluid Mech"},{"key":"2883_CR20","doi-asserted-by":"publisher","DOI":"10.1515\/9783110796018","volume-title":"Finite difference methods for nonlinear evolution equations","author":"ZZ Sun","year":"2023","unstructured":"Sun ZZ, Zhang Q, Gao GH (2023) Finite difference methods for nonlinear evolution equations, 8th edn. De Gruyter, Berlin","edition":"8"},{"key":"2883_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2019.121085","volume":"527","author":"MA Taneco-Hern\u00e1ndez","year":"2019","unstructured":"Taneco-Hern\u00e1ndez MA, Morales-Delgado VF, G\u00f3mez-Aguilar JF (2019) Fractional Kuramoto-Sivashinsky equation with power law and stretched Mittag-Leffler kernel. Physica A Stat Mech Appl 527:121085","journal-title":"Physica A Stat Mech Appl"},{"issue":"6","key":"2883_CR22","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1007\/s40314-023-02373-z","volume":"42","author":"Q Tian","year":"2023","unstructured":"Tian Q, Yang X, Zhang H, Xu D (2023) An implicit robust numerical scheme with graded meshes for the modified Burgers model with nonlocal dynamic properties. Comput Appl Math 42(6):246","journal-title":"Comput Appl Math"},{"issue":"2","key":"2883_CR23","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s40819-021-00956-0","volume":"7","author":"P Veeresha","year":"2021","unstructured":"Veeresha P, Prakasha DG (2021) Solution for fractional Kuramoto-Sivashinsky equation using novel computational technique. Int J Appl Comput Math 7(2):33","journal-title":"Int J Appl Comput Math"},{"key":"2883_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10444-021-09848-9","volume":"47","author":"X Wang","year":"2021","unstructured":"Wang X, Zhang Q, Sun Z (2021) The pointwise error estimates of two energy-preserving fourth-order compact schemes for viscous Burgers\u2019 equation. Adv Comput Math 47:1\u201342","journal-title":"Adv Comput Math"},{"issue":"107644","key":"2883_CR25","first-page":"203","volume":"124","author":"X Yang","year":"2022","unstructured":"Yang X, Zhang H (2022) The uniform $$l^1$$ long-time behavior of time discretization for time-fractional partial differential equations with nonsmooth data. Appl Math Lett 124(107644):203\u2013224","journal-title":"Appl Math Lett"},{"key":"2883_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2023.108972","volume":"150","author":"X Yang","year":"2024","unstructured":"Yang X, Zhang Z (2024) On conservative, positivity preserving, nonlinear FV scheme on distorted meshes for the multi-term nonlocal Nagumo-type equations. Appl Math Lett 150:108972","journal-title":"Appl Math Lett"},{"key":"2883_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.camwa.2020.11.015","volume":"82","author":"X Yang","year":"2021","unstructured":"Yang X, Zhang H, Tang J (2021) The OSC solver for the fourth-order sub-diffusion equation with weakly singular solutions. Comput Math Appl 82:1\u201312","journal-title":"Comput Math Appl"},{"key":"2883_CR28","volume":"457","author":"X Yang","year":"2023","unstructured":"Yang X, Wu L, Zhang H (2023) A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity. Appl Math Comput 457:128192","journal-title":"Appl Math Comput"},{"key":"2883_CR29","volume":"436","author":"Y Zhang","year":"2023","unstructured":"Zhang Y, Feng M (2023) A local projection stabilization virtual element method for the time-fractional Burgers equation with high Reynolds numbers. Appl Math Comput 436:127509","journal-title":"Appl Math Comput"},{"key":"2883_CR30","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1007\/s10915-020-01308-8","volume":"85","author":"H Zhang","year":"2020","unstructured":"Zhang H, Yang X, Xu D (2020) An efficient spline collocation method for a nonlinear fourth-order reaction subdiffusion equation. J Sci Comput 85:7","journal-title":"J Sci Comput"},{"key":"2883_CR31","volume":"418","author":"Q Zhang","year":"2022","unstructured":"Zhang Q, Sun C, Fang ZW, Sun HW (2022) Pointwise error estimate and stability analysis of fourth-order compact difference scheme for time-fractional Burgers\u2019 equation. Appl Math Comput 418:126824","journal-title":"Appl Math Comput"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02883-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-024-02883-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02883-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T13:09:41Z","timestamp":1726232981000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-024-02883-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,20]]},"references-count":31,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["2883"],"URL":"https:\/\/doi.org\/10.1007\/s40314-024-02883-4","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,20]]},"assertion":[{"value":"28 November 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 June 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 July 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 August 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"381"}}