{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T04:52:44Z","timestamp":1785473564547,"version":"3.56.0"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T00:00:00Z","timestamp":1743638400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T00:00:00Z","timestamp":1743638400000},"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":[[2025,7]]},"DOI":"10.1007\/s40314-025-03160-8","type":"journal-article","created":{"date-parts":[[2025,4,5]],"date-time":"2025-04-05T01:44:14Z","timestamp":1743817454000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Enhanced numerical solution for time fractional Kuramoto\u2013Sivashinsky dynamics via shifted companion Morgan\u2013Voyce polynomials"],"prefix":"10.1007","volume":"44","author":[{"given":"Panumart","family":"Sawangtong","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mehran","family":"Taghipour","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alireza","family":"Najafi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,4,3]]},"reference":[{"issue":"3","key":"3160_CR1","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1007\/s40995-024-01600-4","volume":"48","author":"M Abbasi","year":"2024","unstructured":"Abbasi M, Ahmadinia M, Hadi P (2024) A stable finite volume method for numerical solution of time-tempered fractional Sine\u2013Gordon equations. Iran J Sci 48(3):637\u2013647","journal-title":"Iran J Sci"},{"key":"3160_CR2","volume-title":"Ordinary and partial differential equations: with special functions, Fourier series, and boundary value problems","author":"RP Agarwal","year":"2008","unstructured":"Agarwal RP, O\u2019Regan D (2008) Ordinary and partial differential equations: with special functions, Fourier series, and boundary value problems. Springer, London"},{"issue":"1","key":"3160_CR3","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1007\/s44198-024-00194-0","volume":"31","author":"HM Ahmed","year":"2024","unstructured":"Ahmed HM, Abd-Elhameed WM (2024) Spectral solutions of specific singular differential equations using a unified spectral Galerkin-collocation algorithm. J Nonlinear Math Phys 31(1):42","journal-title":"J Nonlinear Math Phys"},{"issue":"1","key":"3160_CR4","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s40314-024-03077-8","volume":"44","author":"AA Alikhanov","year":"2025","unstructured":"Alikhanov AA, Yadav P, Singh VK, Asl MS (2025) A high-order compact difference scheme for the multi-term time-fractional Sobolev-type convection\u2013diffusion equation. Comput Appl Math 44(1):115","journal-title":"Comput Appl Math"},{"key":"3160_CR5","volume-title":"The gamma function","author":"E Artin","year":"2015","unstructured":"Artin E (2015) The gamma function. Courier Dover Publications, London"},{"key":"3160_CR6","unstructured":"Ashinsky GS (1998) Nonlinear analysis of hydrodynamic instability in Lamiar flames\u2014I. Derivation of basic equations. In: Dynamics of curved Fronts. Academic Press, London, pp 459\u2013488"},{"key":"3160_CR7","first-page":"1","volume":"2024","author":"AG Atta","year":"2024","unstructured":"Atta AG, Soliman JF, Elsaeed EW, Elsaeed MW, Youssri YH (2024) Spectral collocation algorithm for the fractional Bratu equation via Hexic shifted Chebyshev polynomials. Comput Methods Differ Equ 2024:1","journal-title":"Comput Methods Differ Equ"},{"issue":"7","key":"3160_CR8","doi-asserted-by":"crossref","first-page":"1512","DOI":"10.1080\/00207160.2023.2201642","volume":"100","author":"R Choudhary","year":"2023","unstructured":"Choudhary R, Kumar D (2023) Numerical solution of linear time-fractional Kuramoto\u2013Sivashinsky equation via quintic B-splines. Int J Comput Math 100(7):1512\u20131531","journal-title":"Int J Comput Math"},{"key":"3160_CR9","first-page":"1","volume":"2024","author":"R Choudhary","year":"2024","unstructured":"Choudhary R, Singh S, Das P, Kumar D (2024) A higher order stable numerical approximation for time-fractional non-linear Kuramoto\u2013Sivashinsky equation based on quintic B B-spline. Math Method Appl Sci 2024:1","journal-title":"Math Method Appl Sci"},{"issue":"23","key":"3160_CR10","doi-asserted-by":"crossref","first-page":"4746","DOI":"10.1103\/PhysRevLett.74.4746","volume":"74","author":"R Cuerno","year":"1995","unstructured":"Cuerno R, Barab\u00e1si AL (1995) Dynamic scaling of ion-sputtered surfaces. Phys Rev Lett 74(23):4746","journal-title":"Phys Rev Lett"},{"issue":"9","key":"3160_CR11","doi-asserted-by":"crossref","DOI":"10.1088\/1402-4896\/ad6d02","volume":"99","author":"MH Derakhshan","year":"2024","unstructured":"Derakhshan MH, Mortazavifar SL, Veeresha P, Gomez-Aguilar JF (2024) An efficient hybrid approach for numerical study of two-dimensional time-fractional Cattaneo model with Riesz distributed-order space-fractional operator along with stability analysis. Phys Scr 99(9):095242","journal-title":"Phys Scr"},{"issue":"6","key":"3160_CR12","volume":"99","author":"Shab Fa","year":"2024","unstructured":"Fa Shab, Aljawi S, Bouzgarrou S, Alotaibi FM, Gomez-Aguilar JF (2024) Hybrid finite element and Laplace transform of 2D multi-term fractional order advection\u2013diffusion equation. Phys Scr 99(6):065272","journal-title":"Phys Scr"},{"key":"3160_CR13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.enganabound.2024.02.011","volume":"163","author":"A Habibirad","year":"2024","unstructured":"Habibirad A, Baghani O, Hesameddini E, Heydari MH, Azin H (2024) A meshless method based on the modified moving Kriging interpolation for numerical solution of space-fractional diffusion equation. Eng Anal Bound Elem 163:1\u201311","journal-title":"Eng Anal Bound Elem"},{"issue":"04","key":"3160_CR14","doi-asserted-by":"crossref","first-page":"2340061","DOI":"10.1142\/S0218348X23400613","volume":"31","author":"XL Han","year":"2023","unstructured":"Han XL, Guo T, Nikan O, Avazzadeh Z (2023) Robust implicit difference approach for the time-fractional Kuramoto\u2013Sivashinsky equation with the non-smooth solution. Fractals 31(04):2340061","journal-title":"Fractals"},{"issue":"191\u2013194","key":"3160_CR15","first-page":"19","volume":"15","author":"GM Homsy","year":"1974","unstructured":"Homsy GM (1974) Model equations for wavy viscous film flow. Lect Appl Math 15(191\u2013194):19","journal-title":"Lect Appl Math"},{"key":"3160_CR16","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/978-94-011-5020-0_20","volume":"7","author":"AF Horadam","year":"1998","unstructured":"Horadam AF (1998) New aspects of Morgan\u2013Voyce polynomials. Appl Fibonacci Numbers 7:161\u2013176","journal-title":"Appl Fibonacci Numbers"},{"issue":"2","key":"3160_CR17","doi-asserted-by":"crossref","first-page":"1831","DOI":"10.1002\/mma.6881","volume":"44","author":"M Hosseininia","year":"2021","unstructured":"Hosseininia M, Heydari MH, Hooshmandasl MR, Maalek Ghaini FM, Avazzadeh Z (2021) A numerical method based on the Chebyshev cardinal functions for variable-order fractional version of the fourth-order 2D Kuramoto\u2013Sivashinsky equation. Math Method Appl Sci 44(2):1831\u20131842","journal-title":"Math Method Appl Sci"},{"key":"3160_CR18","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2024.116227","volume":"456","author":"Y Huang","year":"2025","unstructured":"Huang Y, Rad NT, Skandari MHN, Tohidi E (2025) A spectral collocation scheme for solving nonlinear delay distributed-order fractional equations. J Comput Appl Math 456:116227","journal-title":"J Comput Appl Math"},{"issue":"2179","key":"3160_CR19","first-page":"20140932","volume":"471","author":"A Kalogirou","year":"2015","unstructured":"Kalogirou A, Keaveny EE, Papageorgiou DT (2015) An in-depth numerical study of the two-dimensional Kuramoto\u2013Sivashinsky equation. Proc R Soc A Math Phys Eng Sci 471(2179):20140932","journal-title":"Proc R Soc A Math Phys Eng Sci"},{"issue":"03","key":"3160_CR20","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.26637\/MJM0803\/0060","volume":"8","author":"S Kulkarni","year":"2020","unstructured":"Kulkarni S, Takale K, Gaikwad S (2020) Numerical solution of time fractional Kuramoto\u2013Sivashinsky equation by Adomian decomposition method and applications. Malays J Math 8(03):1078\u20131084","journal-title":"Malays J Math"},{"key":"3160_CR21","first-page":"1","volume":"2024","author":"S Kumar","year":"2024","unstructured":"Kumar S, Singh V, Kumar U (2024) Solvability of fractional differential equations with applications of Morgan\u2013Voyce polynomials. Phys Scr 2024:1","journal-title":"Phys Scr"},{"key":"3160_CR22","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1143\/PTPS.64.346","volume":"64","author":"Y Kuramoto","year":"1978","unstructured":"Kuramoto Y (1978) Diffusion-induced chaos in reaction systems. Prog Theor Phys Supp 64:346\u2013367","journal-title":"Prog Theor Phys Supp"},{"issue":"7","key":"3160_CR23","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1103\/PhysRevLett.34.391","volume":"34","author":"RE LaQuey","year":"1975","unstructured":"LaQuey RE, Mahajan SM, Rutherford PH, Tang WM (1975) Nonlinear saturation of the trapped-ion mode. Phys Rev Lett 34(7):391","journal-title":"Phys Rev Lett"},{"key":"3160_CR24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.camwa.2024.12.024","volume":"2025","author":"M Li","year":"2025","unstructured":"Li M, Ge L (2025) Adaptive space-time finite element method for time fractional-order reaction\u2013diffusion equations. J Appl Math Comput 2025:1\u201326","journal-title":"J Appl Math Comput"},{"key":"3160_CR25","volume":"138","author":"L Li","year":"2024","unstructured":"Li L, Chen Z, Du H, Jiang W, Zhang B (2024) A meshless approach based on fractional interpolation theory and improved neural network bases for solving non-smooth solution of 2D fractional reaction\u2013diffusion equation with distributed order. Commun Nonlinear Sci Numer Simul 138:108245","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"3","key":"3160_CR26","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1007\/s10915-024-02556-8","volume":"99","author":"Z Liu","year":"2024","unstructured":"Liu Z, Song M, Liang H (2024) An isoparametric finite element method for time-fractional parabolic equation on 2D curved domain. J Sci Comput 99(3):88","journal-title":"J Sci Comput"},{"issue":"3","key":"3160_CR27","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1007\/BF01025515","volume":"9","author":"AA Nepomnyashchii","year":"1974","unstructured":"Nepomnyashchii AA (1974) Stability of wavy conditions in a film flowing down an inclined plane. Fluid Dyn 9(3):354\u2013359","journal-title":"Fluid Dyn"},{"issue":"3","key":"3160_CR28","first-page":"1","volume":"12","author":"RK Pandey","year":"2021","unstructured":"Pandey RK, Mishra HK (2021) The numerical solution of time fractional Kuramoto\u2013Sivashinsky equations via homotopy analysis fractional Sumudu transform method. Math Eng Sci Aerosp 12(3):1","journal-title":"Math Eng Sci Aerosp"},{"issue":"2","key":"3160_CR29","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.120.024102","volume":"120","author":"J Pathak","year":"2018","unstructured":"Pathak J, Hunt B, Girvan M, Lu Z, Ott E (2018) Model-free prediction of large spatiotemporally chaotic systems from data: a reservoir computing approach. Phys Rev Lett 120(2):024102","journal-title":"Phys Rev Lett"},{"key":"3160_CR30","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2023.114070","volume":"175","author":"P Rahimkhani","year":"2023","unstructured":"Rahimkhani P, Heydari MH (2023) Fractional shifted Morgan\u2013Voyce neural networks for solving fractal\u2013fractional pantograph differential equations. Chaos Solit Fract 175:114070","journal-title":"Chaos Solit Fract"},{"key":"3160_CR31","first-page":"1","volume":"2024","author":"SM Sayed","year":"2024","unstructured":"Sayed SM, Mohamed AS, Abo-Eldahab EM, Youssri YH (2024) A compact combination of second-kind Chebyshev polynomials for Robin boundary value problems and Bratu-type equations. JUmm Al Qura Univ Appll Sci 2024:1\u201318","journal-title":"JUmm Al Qura Univ Appll Sci"},{"key":"3160_CR32","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/978-94-011-4271-7_29","volume":"8","author":"AG Shannon","year":"1999","unstructured":"Shannon AG, Horadam AF (1999) Some relationships among Vieta. Morgan\u2013Voyce and Jacobsthal polynomials. Appl Fibonacci Numbers 8:307\u2013323","journal-title":"Appl Fibonacci Numbers"},{"issue":"1","key":"3160_CR33","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF01024797","volume":"2","author":"VY Shkadov","year":"1967","unstructured":"Shkadov VY (1967) Wave flow regimes of a thin layer of viscous fluid subject to gravity. Fluid Dyn 2(1):29\u201334","journal-title":"Fluid Dyn"},{"issue":"4","key":"3160_CR34","doi-asserted-by":"crossref","first-page":"301","DOI":"10.3390\/fractalfract7040301","volume":"7","author":"HM Srivastava","year":"2023","unstructured":"Srivastava HM, Adel W, Izadi M, El-Sayed AA (2023) Aolving some physics problem involving fractional-order differential equations with the Morgan\u2013Voyce polynomials. Fract Fract 7(4):301","journal-title":"Fract Fract"},{"issue":"1","key":"3160_CR35","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1080\/00150517.1966.12431395","volume":"4","author":"MNS Swamy","year":"1966","unstructured":"Swamy MNS (1966) Properties of the polynomials defined by Morgan\u2013Voyce. Fibonacci Q 4(1):73\u201381","journal-title":"Fibonacci Q"},{"issue":"1","key":"3160_CR36","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1080\/00150517.2000.12428827","volume":"38","author":"MN Swamy","year":"2000","unstructured":"Swamy MN (2000) Rising diagonal polynomials associated with Morgan\u2013Voyce polynomials. Fibonacci Q 38(1):61\u201369","journal-title":"Fibonacci Q"},{"key":"3160_CR37","doi-asserted-by":"crossref","first-page":"6189","DOI":"10.37256\/cm.5420245950","volume":"2024","author":"MA Taema","year":"2024","unstructured":"Taema MA, Youssri YH (2024) Third-kind Chebyshev spectral collocation method for solving models of two interacting biological species. Contemp Math 2024:6189\u20136207","journal-title":"Contemp Math"},{"issue":"2","key":"3160_CR38","first-page":"33","volume":"7","author":"P Veeresha","year":"2021","unstructured":"Veeresha P, Prakasha DG (2021) Solution for fractional Kuramoto\u2013Sivashinsky equation using novel computational technique. Int J Comput Math 7(2):33","journal-title":"Int J Comput Math"},{"issue":"10","key":"3160_CR39","volume":"99","author":"LX Vivas-Cruz","year":"2024","unstructured":"Vivas-Cruz LX, Gonzalez-Calderon A, Taneco-Hernandez MA, Gomez-Aguilar JF (2024) Hybrid finite element and Laplace transform method for efficient numerical solutions of fractional PDEs on graphics units. Phys Scr 99(10):105290","journal-title":"Phys Scr"},{"key":"3160_CR40","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.neunet.2020.02.016","volume":"126","author":"PR Vlachas","year":"2020","unstructured":"Vlachas PR, Pathak J, Hunt BR, Sapsis TP, Girvan M, Ott E, Koumoutsakos P (2020) Backpropagation algorithms and reservoir computing in recurrent neural networks for the forecasting of complex spatiotemporal dynamics. Neural Netw 126:191\u2013217","journal-title":"Neural Netw"},{"issue":"6","key":"3160_CR41","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/s40314-024-02883-4","volume":"43","author":"J Wang","year":"2024","unstructured":"Wang J, Jiang X, Yang X, Zhang H (2024) A new robust compact difference scheme on graded meshes for the time-fractional nonlinear Kuramoto\u2013Sivashinsky equation. Comput Appl Math 43(6):381","journal-title":"Comput Appl Math"},{"issue":"1","key":"3160_CR42","doi-asserted-by":"crossref","first-page":"20240022","DOI":"10.1515\/nleng-2024-0022","volume":"13","author":"YH Youssri","year":"2024","unstructured":"Youssri YH, Atta AG, Abu Waar ZY, Moustafa MO (2024) Petrov\u2013Galerkin method for small deflections in fourth-order beam equations in civil engineering. Nonlinear Eng 13(1):20240022","journal-title":"Nonlinear Eng"},{"issue":"1","key":"3160_CR43","doi-asserted-by":"crossref","first-page":"53","DOI":"10.3390\/fractalfract8010053","volume":"8","author":"J Zhang","year":"2024","unstructured":"Zhang J, Yang Q (2024) The finite volume element method for time fractional generalized Burgers\u2019 equation. Fractal Fract 8(1):53","journal-title":"Fractal Fract"},{"key":"3160_CR44","volume":"159","author":"X Zhang","year":"2025","unstructured":"Zhang X, Feng Y, Luo Z, Liu J (2025) A spatial sixth-order numerical scheme for solving fractional partial differential equation. Appl Math Lett 159:109265","journal-title":"Appl Math Lett"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03160-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-025-03160-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03160-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T14:10:53Z","timestamp":1747663853000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-025-03160-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,3]]},"references-count":44,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["3160"],"URL":"https:\/\/doi.org\/10.1007\/s40314-025-03160-8","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,3]]},"assertion":[{"value":"3 November 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 February 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 February 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 April 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"214"}}