{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T17:41:13Z","timestamp":1783705273373,"version":"3.55.0"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T00:00:00Z","timestamp":1715299200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T00:00:00Z","timestamp":1715299200000},"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":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2024,8]]},"DOI":"10.1007\/s12190-024-02098-0","type":"journal-article","created":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T03:35:51Z","timestamp":1715312151000},"page":"3661-3684","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A numerical technique based on Legendre wavelet for linear and nonlinear hyperbolic telegraph equation"],"prefix":"10.1007","volume":"70","author":[{"given":"Basharat","family":"Hussain","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mo","family":"Faheem","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arshad","family":"Khan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,5,10]]},"reference":[{"key":"2098_CR1","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.cpc.2015.03.021","volume":"193","author":"R Jiwari","year":"2015","unstructured":"Jiwari, R.: Lagrange interpolation and modified cubic B-spline differential quadrature methods for solving hyperbolic partial differential equations with Dirichlet and Neumann boundary conditions. Comput. Phys. Commun. 193, 55\u201365 (2015)","journal-title":"Comput. Phys. Commun."},{"key":"2098_CR2","first-page":"976","volume":"244","author":"R Mittal","year":"2014","unstructured":"Mittal, R., Bhatia, R.: A numerical study of two dimensional hyperbolic telegraph equation by modified B-spline differential quadrature method. Appl. Math. Comput. 244, 976\u2013997 (2014)","journal-title":"Appl. Math. Comput."},{"issue":"3","key":"2098_CR3","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1063\/1.369258","volume":"85","author":"P Jordan","year":"1999","unstructured":"Jordan, P., Puri, A.: Digital signal propagation in dispersive media. J. Appl. Phys. 85(3), 1273\u20131282 (1999)","journal-title":"J. Appl. Phys."},{"key":"2098_CR4","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1016\/j.cjph.2019.04.006","volume":"59","author":"ME Koksal","year":"2019","unstructured":"Koksal, M.E., Senol, M., Unver, A.K.: Numerical simulation of power transmission lines. Chin. J. Phys. 59, 507\u2013524 (2019)","journal-title":"Chin. J. Phys."},{"key":"2098_CR5","first-page":"9","volume":"11","author":"J Banasiak","year":"1998","unstructured":"Banasiak, J., Mika, J.R.: Singularly perturbed telegraph equations with applications in the random walk theory. Int. J. Stoch. Anal. 11, 9\u201328 (1998)","journal-title":"Int. J. Stoch. Anal."},{"issue":"10","key":"2098_CR6","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1080\/0020716031000112312","volume":"80","author":"DJ Evans","year":"2003","unstructured":"Evans, D.J., Bulut, H.: The numerical solution of the telegraph equation by the alternating group explicit (AGE) method. Int. J. Comput. Math. 80(10), 1289\u20131297 (2003)","journal-title":"Int. J. Comput. Math."},{"issue":"6","key":"2098_CR7","doi-asserted-by":"crossref","first-page":"7918","DOI":"10.1103\/PhysRevE.62.7918","volume":"62","author":"P Jordan","year":"2000","unstructured":"Jordan, P., Meyer, M.R., Puri, A.: Causal implications of viscous damping in compressible fluid flows. Phys. Rev. E 62(6), 7918 (2000)","journal-title":"Phys. Rev. E"},{"issue":"6","key":"2098_CR8","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1088\/0266-5611\/9\/6\/013","volume":"9","author":"V Weston","year":"1993","unstructured":"Weston, V., He, S.: Wave splitting of the telegraph equation in R$$^3$$ and its application to inverse scattering. Inverse Prob. 9(6), 789 (1993)","journal-title":"Inverse Prob."},{"issue":"4","key":"2098_CR9","doi-asserted-by":"crossref","first-page":"59","DOI":"10.3390\/math6040059","volume":"6","author":"W Alharbi","year":"2018","unstructured":"Alharbi, W., Petrovskii, S.: Critical domain problem for the reaction-telegraph equation model of population dynamics. Mathematics 6(4), 59 (2018)","journal-title":"Mathematics"},{"issue":"12","key":"2098_CR10","doi-asserted-by":"crossref","first-page":"2061","DOI":"10.1080\/00207160801965271","volume":"86","author":"R Mohanty","year":"2009","unstructured":"Mohanty, R.: New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations. Int. J. Comput. Math. 86(12), 2061\u20132071 (2009)","journal-title":"Int. J. Comput. Math."},{"issue":"3","key":"2098_CR11","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1080\/00207161003611242","volume":"88","author":"B B\u00fclb\u00fcl","year":"2011","unstructured":"B\u00fclb\u00fcl, B., Sezer, M.: Taylor polynomial solution of hyperbolic type partial differential equations with constant coefficients. Int. J. Comput. Math. 88(3), 533\u2013544 (2011)","journal-title":"Int. J. Comput. Math."},{"key":"2098_CR12","doi-asserted-by":"crossref","DOI":"10.1155\/2014\/526814","volume":"2014","author":"R Mittal","year":"2014","unstructured":"Mittal, R., Bhatia, R.: A collocation method for numerical solution of hyperbolic telegraph equation with Neumann boundary conditions. Int. J. Comput. Math. 2014, 526814 (2014)","journal-title":"Int. J. Comput. Math."},{"issue":"1","key":"2098_CR13","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.enganabound.2009.07.002","volume":"34","author":"M Dehghan","year":"2010","unstructured":"Dehghan, M., Ghesmati, A.: Solution of the second-order one-dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation (DRBIE) method. Eng. Anal. Boundary Elem. 34(1), 51\u201359 (2010)","journal-title":"Eng. Anal. Boundary Elem."},{"issue":"6","key":"2098_CR14","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1080\/00207721.2010.547626","volume":"43","author":"M Hosseini","year":"2012","unstructured":"Hosseini, M., Mohyud-Din, S.T., Nakhaeei, A.: New Rothe-wavelet method for solving telegraph equations. Int. J. Syst. Sci. 43(6), 1171\u20131176 (2012)","journal-title":"Int. J. Syst. Sci."},{"issue":"2","key":"2098_CR15","first-page":"83","volume":"7","author":"M Dosti","year":"2012","unstructured":"Dosti, M., Nazemi, A.: Quartic B-spline collocation method for solving one-dimensional hyperbolic telegraph equation. J. Inf. Comput. Sci. 7(2), 83\u201390 (2012)","journal-title":"J. Inf. Comput. Sci."},{"issue":"5\u20136","key":"2098_CR16","doi-asserted-by":"crossref","first-page":"1597","DOI":"10.1016\/j.apm.2013.09.013","volume":"38","author":"MH Heydari","year":"2014","unstructured":"Heydari, M.H., Hooshmandasl, M., Ghaini, F.M.: A new approach of the Chebyshev wavelets method for partial differential equations with boundary conditions of the telegraph type. Appl. Math. Model. 38(5\u20136), 1597\u20131606 (2014)","journal-title":"Appl. Math. Model."},{"key":"2098_CR17","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.enganabound.2014.04.006","volume":"47","author":"S Abbasbandy","year":"2014","unstructured":"Abbasbandy, S., Ghehsareh, H.R., Hashim, I., Alsaedi, A.: A comparison study of meshfree techniques for solving the two-dimensional linear hyperbolic telegraph equation. Eng. Anal. Boundary Elem. 47, 10\u201320 (2014)","journal-title":"Eng. Anal. Boundary Elem."},{"issue":"1","key":"2098_CR18","first-page":"57","volume":"17","author":"M Sari","year":"2014","unstructured":"Sari, M., Gunay, A., Gurarslan, G.: A solution to the telegraph equation by using DGJ method. Int. J. Nonlinear Sci. 17(1), 57\u201366 (2014)","journal-title":"Int. J. Nonlinear Sci."},{"issue":"1","key":"2098_CR19","doi-asserted-by":"crossref","first-page":"293","DOI":"10.2478\/amns.2020.1.00027","volume":"5","author":"D Arslan","year":"2020","unstructured":"Arslan, D.: The numerical study of a hybrid method for solving telegraph equation. Appl. Math. Nonlinear Sci. 5(1), 293\u2013302 (2020)","journal-title":"Appl. Math. Nonlinear Sci."},{"issue":"1","key":"2098_CR20","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1002\/num.21996","volume":"32","author":"KT Elgindy","year":"2016","unstructured":"Elgindy, K.T.: High-order numerical solution of second-order one-dimensional hyperbolic telegraph equation using a shifted Gegenbauer pseudospectral method. Numer. Methods Partial Differ. Equ. 32(1), 307\u2013349 (2016)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"10","key":"2098_CR21","doi-asserted-by":"crossref","first-page":"1716","DOI":"10.1016\/j.aml.2011.04.026","volume":"24","author":"B B\u00fclb\u00fcl","year":"2011","unstructured":"B\u00fclb\u00fcl, B., Sezer, M.: A Taylor matrix method for the solution of a two-dimensional linear hyperbolic equation. Appl. Math. Lett. 24(10), 1716\u20131720 (2011)","journal-title":"Appl. Math. Lett."},{"key":"2098_CR22","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.jcp.2015.10.027","volume":"305","author":"JA Acebr\u00f3n","year":"2016","unstructured":"Acebr\u00f3n, J.A., Ribeiro, M.A.: A Monte Carlo method for solving the one-dimensional telegraph equations with boundary conditions. J. Comput. Phys. 305, 29\u201343 (2016)","journal-title":"J. Comput. Phys."},{"key":"2098_CR23","volume":"2013","author":"M Inc","year":"2013","unstructured":"Inc, M., Akg\u00fcl, A., K\u0131l\u0131\u00e7man, A.: Numerical solutions of the second-order one-dimensional telegraph equation based on reproducing kernel Hilbert space method. Abstr. Appl. Anal. 2013, 768963 (2013)","journal-title":"Abstr. Appl. Anal."},{"issue":"2","key":"2098_CR24","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1108\/09615531311293515","volume":"23","author":"B Raftari","year":"2013","unstructured":"Raftari, B., Khosravi, H., Yildirim, A.: Homotopy analysis method for the one-dimensional hyperbolic telegraph equation with initial conditions. Int. J. Numer. Methods Heat Fluid Flow 23(2), 355\u2013372 (2013)","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"issue":"6","key":"2098_CR25","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1002\/num.22074","volume":"32","author":"W Abd-Elhameed","year":"2016","unstructured":"Abd-Elhameed, W., Doha, E., Youssri, Y., Bassuony, M.: New Tchebyshev-Galerkin operational matrix method for solving linear and nonlinear hyperbolic telegraph type equations. Numer. Methods Partial Differ. Equ. 32(6), 1553\u20131571 (2016)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"03","key":"2098_CR26","doi-asserted-by":"crossref","first-page":"1750026","DOI":"10.1142\/S0219876217500268","volume":"14","author":"A Mardani","year":"2017","unstructured":"Mardani, A., Hooshmandasl, M., Hosseini, M., Heydari, M.: Moving least squares (MLS) method for the nonlinear hyperbolic telegraph equation with variable coefficients. Int. J. Comput. Methods 14(03), 1750026 (2017)","journal-title":"Int. J. Comput. Methods"},{"issue":"7","key":"2098_CR27","doi-asserted-by":"crossref","first-page":"1964","DOI":"10.1016\/j.camwa.2010.07.030","volume":"60","author":"M Lakestani","year":"2010","unstructured":"Lakestani, M., Saray, B.N.: Numerical solution of telegraph equation using interpolating scaling functions. Comput. Math. Appl. 60(7), 1964\u20131972 (2010)","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"2098_CR28","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1080\/00207160211918","volume":"79","author":"R Mohanty","year":"2002","unstructured":"Mohanty, R., Jain, M.K., Arora, U.: An unconditionally stable ADI method for the linear hyperbolic equation in three space dimensions. Int. J. Comput. Math. 79(1), 133\u2013142 (2002)","journal-title":"Int. J. Comput. Math."},{"issue":"4","key":"2098_CR29","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/j.enganabound.2009.10.010","volume":"34","author":"M Dehghan","year":"2010","unstructured":"Dehghan, M., Ghesmati, A.: Combination of meshless local weak and strong (MLWS) forms to solve the two dimensional hyperbolic telegraph equation. Eng. Anal. Boundary Elem. 34(4), 324\u2013336 (2010)","journal-title":"Eng. Anal. Boundary Elem."},{"issue":"2","key":"2098_CR30","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1002\/num.20357","volume":"25","author":"M Dehghan","year":"2009","unstructured":"Dehghan, M., Shokri, A.: A meshless method for numerical solution of a linear hyperbolic equation with variable coefficients in two space dimensions. Numer. Methods Partial Differ. Equ. Int. J. 25(2), 494\u2013506 (2009)","journal-title":"Numer. Methods Partial Differ. Equ. Int. J."},{"issue":"2","key":"2098_CR31","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1016\/j.cam.2009.01.001","volume":"230","author":"H Ding","year":"2009","unstructured":"Ding, H., Zhang, Y.: A new fourth-order compact finite difference scheme for the two-dimensional second-order hyperbolic equation. J. Comput. Appl. Math. 230(2), 626\u2013632 (2009)","journal-title":"J. Comput. Appl. Math."},{"issue":"4","key":"2098_CR32","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1108\/EC-05-2016-0179","volume":"34","author":"AS Alshomrani","year":"2017","unstructured":"Alshomrani, A.S., Pandit, S., Alzahrani, A.K., Alghamdi, M.S., Jiwari, R.: A numerical algorithm based on modified cubic trigonometric B-spline functions for computational modelling of hyperbolic-type wave equations. Eng. Comput. 34(4), 1257\u20131276 (2017)","journal-title":"Eng. Comput."},{"issue":"1","key":"2098_CR33","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1080\/00036811.2014.998654","volume":"95","author":"J Rashidinia","year":"2016","unstructured":"Rashidinia, J., Jokar, M.: Application of polynomial scaling functions for numerical solution of telegraph equation. Appl. Anal. 95(1), 105\u2013123 (2016)","journal-title":"Appl. Anal."},{"key":"2098_CR34","first-page":"83","volume":"287","author":"\u015e Y\u00fczba\u015f\u0131","year":"2016","unstructured":"Y\u00fczba\u015f\u0131, \u015e: Numerical solutions of hyperbolic telegraph equation by using the Bessel functions of first kind and residual correction. Appl. Math. Comput. 287, 83\u201393 (2016)","journal-title":"Appl. Math. Comput."},{"issue":"3","key":"2098_CR35","doi-asserted-by":"crossref","first-page":"2060","DOI":"10.1002\/num.22957","volume":"39","author":"E Kirli","year":"2023","unstructured":"Kirli, E., Irk, D., Zorsahin Gorgulu, M.: High order accurate method for the numerical solution of the second order linear hyperbolic telegraph equation. Numer. Methods Partial Differ. Equ. 39(3), 2060\u20132072 (2023)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"5","key":"2098_CR36","doi-asserted-by":"crossref","first-page":"1086","DOI":"10.1002\/num.20388","volume":"25","author":"A Ashyralyev","year":"2009","unstructured":"Ashyralyev, A., Koksal, M.E.: On the numerical solution of hyperbolic PDEs with variable space operator. Numer. Methods Partial Differ. Equ. Int. J. 25(5), 1086\u20131099 (2009)","journal-title":"Numer. Methods Partial Differ. Equ. Int. J."},{"issue":"1","key":"2098_CR37","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/S0893-9659(04)90019-5","volume":"17","author":"R Mohanty","year":"2004","unstructured":"Mohanty, R.: An unconditionally stable difference scheme for the one-space-dimensional linear hyperbolic equation. Appl. Math. Lett. 17(1), 101\u2013105 (2004)","journal-title":"Appl. Math. Lett."},{"issue":"4","key":"2098_CR38","first-page":"837","volume":"10","author":"A Babu","year":"2022","unstructured":"Babu, A., Han, B., Asharaf, N.: Numerical solution of the hyperbolic telegraph equation using cubic B-spline-based differential quadrature of high accuracy. Comput. Methods Differ. Equ. 10(4), 837\u2013859 (2022)","journal-title":"Comput. Methods Differ. Equ."},{"issue":"6","key":"2098_CR39","doi-asserted-by":"crossref","first-page":"1962","DOI":"10.1002\/num.22512","volume":"36","author":"M Asif","year":"2020","unstructured":"Asif, M., Haider, N., Al-Mdallal, Q., Khan, I.: A Haar wavelet collocation approach for solving one and two-dimensional second-order linear and nonlinear hyperbolic telegraph equations. Numer. Methods Partial Differ. Equ. 36(6), 1962\u20131981 (2020)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"4","key":"2098_CR40","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1080\/00207720120227","volume":"32","author":"M Razzaghi","year":"2001","unstructured":"Razzaghi, M., Yousefi, S.: The Legendre wavelets operational matrix of integration. Int. J. Syst. Sci. 32(4), 495\u2013502 (2001)","journal-title":"Int. J. Syst. Sci."},{"issue":"3","key":"2098_CR41","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.cpc.2005.01.016","volume":"168","author":"M Shamsi","year":"2005","unstructured":"Shamsi, M., Razzaghi, M.: Solution of Hallen\u2019s integral equation using multiwavelets. Comput. Phys. Commun. 168(3), 187\u2013197 (2005)","journal-title":"Comput. Phys. Commun."},{"key":"2098_CR42","doi-asserted-by":"crossref","DOI":"10.1155\/MPE\/2006\/96184","volume":"2006","author":"M Lakestani","year":"2006","unstructured":"Lakestani, M., Razzaghi, M., Dehghan, M.: Semiorthogonal spline wavelets approximation for Fredholm integro-differential equations. Math. Probl. Eng. 2006, 096184 (2006)","journal-title":"Math. Probl. Eng."},{"issue":"2","key":"2098_CR43","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1002\/cpa.3160440202","volume":"44","author":"G Beylkin","year":"1991","unstructured":"Beylkin, G., Coifman, R., Rokhlin, V.: Fast wavelet transforms and numerical algorithms I. Commun. Pure Appl. Math. 44(2), 141\u2013183 (1991)","journal-title":"Commun. Pure Appl. Math."},{"key":"2098_CR44","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1186\/s13662-020-02965-7","volume":"2020","author":"M Faheem","year":"2020","unstructured":"Faheem, M., Khan, A., El-Zahar, E.: On some wavelet solutions of singular differential equations arising in the modeling of chemical and biochemical phenomena. Adv. Differ. Equ. 2020, 526 (2020)","journal-title":"Adv. Differ. Equ."},{"issue":"6","key":"2098_CR45","doi-asserted-by":"crossref","first-page":"2850","DOI":"10.1108\/EC-04-2020-0218","volume":"38","author":"A Khan","year":"2021","unstructured":"Khan, A., Faheem, M., Raza, A.: Solution of third-order Emden-Fowler-type equations using wavelet methods. Eng. Comput. 38(6), 2850\u20132881 (2021)","journal-title":"Eng. Comput."},{"key":"2098_CR46","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.camwa.2022.10.014","volume":"128","author":"M Faheem","year":"2022","unstructured":"Faheem, M., Khan, A., Wong, P.J.: A Legendre wavelet collocation method for 1D and 2D coupled time-fractional nonlinear diffusion system. Comput. Math. Appl. 128, 214\u2013238 (2022)","journal-title":"Comput. Math. Appl."},{"key":"2098_CR47","first-page":"715","volume":"256","author":"PK Sahu","year":"2015","unstructured":"Sahu, P.K., Ray, S.S.: Legendre wavelets operational method for the numerical solutions of nonlinear Volterra integro-differential equations system. Appl. Math. Comput. 256, 715\u2013723 (2015)","journal-title":"Appl. Math. Comput."},{"key":"2098_CR48","first-page":"353","volume":"247","author":"F Zhou","year":"2014","unstructured":"Zhou, F., Xu, X.: Numerical solution of the convection diffusion equations by the second kind Chebyshev wavelets. Appl. Math. Comput. 247, 353\u2013367 (2014)","journal-title":"Appl. Math. Comput."},{"issue":"7\u20138","key":"2098_CR49","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1515\/ijnsns-2020-0103","volume":"23","author":"M Faheem","year":"2022","unstructured":"Faheem, M., Raza, A., Khan, A.: Wavelet collocation methods for solving neutral delay differential equations. Int. J. Nonlinear Sci. Numer. Simul. 23(7\u20138), 1129\u20131156 (2022)","journal-title":"Int. J. Nonlinear Sci. Numer. Simul."},{"key":"2098_CR50","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.matcom.2020.08.018","volume":"180","author":"M Faheem","year":"2021","unstructured":"Faheem, M., Raza, A., Khan, A.: Collocation methods based on Gegenbauer and Bernoulli wavelets for solving neutral delay differential equations. Math. Comput. Simul. 180, 72\u201392 (2021)","journal-title":"Math. Comput. Simul."},{"issue":"4","key":"2098_CR51","doi-asserted-by":"crossref","first-page":"558","DOI":"10.3390\/math8040558","volume":"8","author":"S Kumar","year":"2020","unstructured":"Kumar, S., Ahmadian, A., Kumar, R., Kumar, D., Singh, J., Baleanu, D., Salimi, M.: An efficient numerical method for fractional SIR epidemic model of infectious disease by using Bernstein wavelets. Mathematics 8(4), 558 (2020)","journal-title":"Mathematics"},{"key":"2098_CR52","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.apnum.2021.05.019","volume":"168","author":"AK Verma","year":"2021","unstructured":"Verma, A.K., Rawani, M.K., Cattani, C.: A numerical scheme for a class of generalized Burgers\u2019 equation based on Haar wavelet nonstandard finite difference method. Appl. Numer. Math. 168, 41\u201354 (2021)","journal-title":"Appl. Numer. Math."},{"key":"2098_CR53","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/978-1-4612-0001-7_7","volume-title":"Multiresolution Analysis","author":"DF Walnut","year":"2004","unstructured":"Walnut, D.F.: Multiresolution Analysis, pp. 163\u2013214. Birkh\u00e4user Boston, Boston (2004). https:\/\/doi.org\/10.1007\/978-1-4612-0001-7_7"},{"key":"2098_CR54","first-page":"28","volume":"281","author":"S Sharifi","year":"2016","unstructured":"Sharifi, S., Rashidinia, J.: Numerical solution of hyperbolic telegraph equation by cubic B-spline collocation method. Appl. Math. Comput. 281, 28\u201338 (2016)","journal-title":"Appl. Math. Comput."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-024-02098-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-024-02098-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-024-02098-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T17:22:05Z","timestamp":1721755325000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-024-02098-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,10]]},"references-count":54,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,8]]}},"alternative-id":["2098"],"URL":"https:\/\/doi.org\/10.1007\/s12190-024-02098-0","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,10]]},"assertion":[{"value":"3 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 April 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 April 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 May 2024","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 declare that they have no financial or non-financial Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}