RETRACTED ARTICLE: Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

[1]C. K. Chui, Wavelets: A Mathematical Tool for Signal Analysis, SIAM, Philadelphia, PA., 1997.ChuiC. K.Wavelets: A Mathematical Tool for Signal AnalysisSIAMPhiladelphia, PA1997Search in Google Scholar

[2]G. Beylkin, R. Coifman, V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Commun. Pure Appl. Math., 44 (1991), 141–183.BeylkinG.CoifmanR.RokhlinV.Fast wavelet transforms and numerical algorithms ICommun. Pure Appl. Math.441991141183Search in Google Scholar

[3]Ü. Lepik, E. Tamme, Application of the Haar wavelets for solution of linear integral Equations, Ant. Turk–Dynam. Sys. Appl. Proce., (2005), 395–407.LepikÜ.TammeE.Application of the Haar wavelets for solution of linear integral EquationsAnt. Turk–Dynam. Sys. Appl. Proce.2005395407Search in Google Scholar

[4]K. Maleknejad, M.T. Kajani, Y. Mahmoudi, Numerical solution of linear Fredholm and Volterra integral equation of the second kind by using Legendre wavelets, J. Kybernet., 32 (2003), 1530-1539.MaleknejadK.KajaniM.T.MahmoudiY.Numerical solution of linear Fredholm and Volterra integral equation of the second kind by using Legendre waveletsJ. Kybernet.32200315301539Search in Google Scholar

[5]K. Maleknejad, F. Mirzaee, Using rationalized haar wavelet for solving linear integral equations, App. Math. Comp., 160 (2005), 579–587.MaleknejadK.MirzaeeF.Using rationalized haar wavelet for solving linear integral equationsApp. Math. Comp.1602005579587Search in Google Scholar

[6]K. Maleknejad, M. Yousefi, Numerical solution of the integral equation of the second kind by using wavelet bases of hermite cubic splines, App. Math. Comp., 183 (2006), 134-141.MaleknejadK.YousefiM.Numerical solution of the integral equation of the second kind by using wavelet bases of hermite cubic splinesApp. Math. Comp.1832006134141Search in Google Scholar

[7]K. Maleknejad, T. Lotfi, Y. Rostami, Numerical computational method in solving fredholm integral equations of the second kind by using coifman wavelet, App. Math. Comp., 186 (2007), 212-218.MaleknejadK.LotfiT.RostamiY.Numerical computational method in solving fredholm integral equations of the second kind by using coifman waveletApp. Math. Comp.1862007212218Search in Google Scholar

[8]S. Yousefi, A. Banifatemi, Numerical solution of Fredholm integral equations by using CAS wavelets, App. Math. Comp., 183 (2006), 458-463.YousefiS.BanifatemiA.Numerical solution of Fredholm integral equations by using CAS waveletsApp. Math. Comp.1832006458463Search in Google Scholar

[9]S. C. Shiralashetti, R. A. Mundewadi, Bernoulli Wavelet Based Numerical Method for Solving Fredholm Integral Equations of the Second Kind, J. Inform. Comp. Sci., 11(2) (2016), 111-119.ShiralashettiS. C.MundewadiR. A.Bernoulli Wavelet Based Numerical Method for Solving Fredholm Integral Equations of the Second KindJ. Inform. Comp. Sci.1122016111119Search in Google Scholar

[10]S. A. Yousefi, Numerical solution of Abel’s integral equation by using Legendre wavelets, Appl. Math. Comp., 175 (2006), 574–80.YousefiS. A.Numerical solution of Abel’s integral equation by using Legendre waveletsAppl. Math. Comp.175200657480Search in Google Scholar

[11]S. Sohrabi, Comparison Chebyshev wavelets method with BPFs method for solving Abel’s integral equation, Ain Shams Eng. J., 2 (2011), 249–254.SohrabiS.Comparison Chebyshev wavelets method with BPFs method for solving Abel’s integral equationAin Shams Eng. J.22011249254Search in Google Scholar

[12]A. M. Wazwaz, Linear and nonlinear integral equations: methods and applications, Berlin: Higher Education, Beijing, Springer, 2011.WazwazA. M.Linear and nonlinear integral equations: methods and applicationsBerlin: Higher Education, BeijingSpringer2011Search in Google Scholar

[13]A. M. Wazwaz, A first course in integral equations, Singapore: World Scientific Publishing, 1997.WazwazA. M.A first course in integral equationsSingaporeWorld Scientific Publishing1997Search in Google Scholar

[14]R. Gorenflo, S. Vessella, Abel integral equations, analysis and applications, In: Lecture notes in mathematics, Heidelberg: Springer, 1991.GorenfloR.VessellaS.Abel integral equations, analysis and applicationsLecture notes in mathematicsHeidelbergSpringer1991Search in Google Scholar

[15]C.T.H. Baker, The numerical treatment of integral equations, Clarendon Press, Oxford, 1977.BakerC.T.H.The numerical treatment of integral equationsClarendon PressOxford1977Search in Google Scholar

[16]S.C. Shiralashetti, S. Kumbinarasaiah, Theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear Lane–Emden type equations, Appl. Math. Comput., 315 (2017), 591–602.ShiralashettiS.C.KumbinarasaiahS.Theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear Lane–Emden type equationsAppl. Math. Comput.3152017591602Search in Google Scholar

[17]H. Brunner, Collocation methods for Volterra integral and related functional differential equations, Cambridge Monographs on Applied and Computational Mathematics, Cambridge Univ. Press, Cambridge, 2004.BrunnerH.Collocation methods for Volterra integral and related functional differential equationsCambridge Monographs on Applied and Computational MathematicsCambridge Univ. PressCambridge2004Search in Google Scholar

[18]S. Noeiaghdam, E. Zarei, H. B. Kelishami, Homotopy analysis transform method for solving Abel’s integral equations of the first kind, Ain Shams Eng. J., 7 (2016), 483–495.NoeiaghdamS.ZareiE.KelishamiH. B.Homotopy analysis transform method for solving Abel’s integral equations of the first kindAin Shams Eng. J.72016483495Search in Google Scholar

[19]N. Zeilon, Sur quelques points de la theorie de l’equation integrale d’Abel, Arkiv Mat Astr Fysik, 18 (1924), 1–19.ZeilonN.Sur quelques points de la theorie de l’equation integrale d’AbelArkiv Mat Astr Fysik181924119Search in Google Scholar

[20]C.T.H. Baker, The numerical treatment of integral equations, Oxford: Clarendon Press, 1977.BakerC.T.H.The numerical treatment of integral equationsOxfordClarendon Press1977Search in Google Scholar

[21]P. Baratella, A. P. Orsi, A new approach to the numerical solution of weakly singular Volterra integral equations, J. Comput. Appl. Math., 163(2) (2004), 401–418.BaratellaP.OrsiA. P.A new approach to the numerical solution of weakly singular Volterra integral equationsJ. Comput. Appl. Math.16322004401418Search in Google Scholar

[22][22] E. Babolian, A. Salimi Shamloo, Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions, J. Comp. Appl. Math., 214 (2008), 495–508.[22]BabolianE.SalimiShamloo A.Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functionsJ. Comp. Appl. Math.2142008495508Search in Google Scholar

[23]A. Shahsavaran, M. R. Moazami Goudarzi, O. Moradtalab, Solving Abel’s integral equation of the first kind using piecewise constant functions and Taylor expansion by collocation method, In: 40th Annual Iranian mathematics conference.ShahsavaranA.MoazamiGoudarzi M. R.MoradtalabO.Solving Abel’s integral equation of the first kind using piecewise constant functions and Taylor expansion by collocation method40th Annual Iranian mathematics conferenceSearch in Google Scholar

[24]A. Ali, M.A. Iqbal, S.T. Mohyud-Din, Hermites wavelets method for Boundary Value problems, Inter. J. Modern Appl. Phy., 3(1) (2013), 38-47.AliA.IqbalM.A.Mohyud-DinS.T.Hermites wavelets method for Boundary Value problemsInter. J. Modern Appl. Phy.3120133847Search in Google Scholar

[25]M.H. Kantli, S.C. Shiralashetti, Finite difference Wavelet–Galerkin method for the numerical solution of elastohydrodynamic lubrication problems, Journal of Analysis, 26(2) (2018), 285-295.KantliM.H.ShiralashettiS.C.Finite difference Wavelet–Galerkin method for the numerical solution of elastohydrodynamic lubrication problemsJournal of Analysis2622018285295Search in Google Scholar

[26]N.M. Bujurke, M.H. Kantli, B.M. Shettar, Jacobian free Newton-GMRES method for the solution of elastohydrodynamic grease lubrication in line contact using wavelet based pre-conditioners, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 88(2) (2018), 247-265.BujurkeN.M.KantliM.H.ShettarB.M.Jacobian free Newton-GMRES method for the solution of elastohydrodynamic grease lubrication in line contact using wavelet based pre-conditioners, Proceedings of the National Academy of SciencesIndia Section A: Physical Sciences8822018247265Search in Google Scholar

[27]N.M. Bujurke, M. H. Kantli, B.M. Shettar, Wavelet preconditioned Newton-Krylov method for elastohydrodynamic lubrication of line contact problems, Applied Mathematical Modelling, 46 (2017), 285-298.BujurkeN.M.KantliM. H.ShettarB.M.Wavelet preconditioned Newton-Krylov method for elastohydrodynamic lubrication of line contact problemsApplied Mathematical Modelling462017285298Search in Google Scholar

[28]S.C. Shiralashetti, M.H. Kantli, A.B. Deshi, A new wavelet multigrid method for the numerical solution of elliptic type differential equations, Alexandria Engineering Journal, 57 (2018), 203-209.ShiralashettiS.C.KantliM.H.DeshiA.B.A new wavelet multigrid method for the numerical solution of elliptic type differential equationsAlexandria Engineering Journal572018203209Search in Google Scholar