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A Comparative Study on Haar Wavelet and Hosaya Polynomial for the numerical solution of Fredholm integral equations


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A.M. Wazwaz. A First Course in Integral Equations. WSPC. New Jersey. 1997.WazwazA.M.A First Course in Integral EquationsWSPC. New Jersey199710.1142/3444Search in Google Scholar

U. Lepik, E. Tamme, Application of the Haar wavelets for solution of linear integral equations, in: Dynamical Systems and Applications, Antala. Proce. (2004) 494-507.LepikU.TammeE. Application of the Haar wavelets for solution of linear integral equations, in: Dynamical Systems and Applications, Antala. Proce2004494507Search in Google Scholar

K. Maleknejad, Y. Mahmoudi, Numerical solution of linear Fredholm integral equation by using hybrid Taylor and Block-Pulse functions, App. Math. Comp. 149 (2004) 799-806.MaleknejadK.MahmoudiY.Numerical solution of linear Fredholm integral equation by using hybrid Taylor and Block-Pulse functionsApp. Math. Comp149200479980610.1016/S0096-3003(03)00180-2Search in Google Scholar

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. Comp160200557958710.1016/j.amc.2003.11.036Search in Google Scholar

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. Comp183200613414110.1016/j.amc.2006.05.104Search in Google Scholar

M. S. Muthuvalu, J. Sulaiman, Half-Sweep Arithmetic Mean method with composite trapezoidal scheme for solving linear fredholm integral equations, App. Math. Comp. 217 (2011) 5442-5448.MuthuvaluM. S.SulaimanJ.Half-Sweep Arithmetic Mean method with composite trapezoidal scheme for solving linear fredholm integral equationsApp. Math. Comp21720115442544810.1016/j.amc.2010.12.013Search in Google Scholar

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 I, CommunPure Appl. Math44199114118310.1002/cpa.3160440202Search in Google Scholar

C. K. Chui, Wavelets: A Mathematical Tool for Signal Analysis, SIAM, Philadelphia, PA, 1997.ChuiC. K.Wavelets: A Mathematical Tool for Signal Analysis, SIAMPhiladelphia, PA199710.1137/1.9780898719727Search in Google Scholar

C.F. Chen, C.H. Hsiao, Haar wavelet method for solving lumped and distributed parameter systems, IEEE Proc. Pt. D. 144 (1) (1997) 87-94.ChenC.F.HsiaoC.H.Haar wavelet method for solving lumped and distributed parameter systemsIEEE Proc. Pt. D14411997879410.1049/ip-cta:19970702Search in Google Scholar

N. M. Bujurke, S. C. Shiralashetti, C. S. Salimath, Numerical solution of stiff systems from non-linear dynamics using single term haar wavelet series, Inter. Jour. Nonlin. Dynam. 51 (2008) 595-605.BujurkeN. M.ShiralashettiS. C.SalimathC. S.Numerical solution of stiff systems from non-linear dynamics using single term haar wavelet seriesInter. Jour. Nonlin. Dynam51200859560510.1007/s11071-007-9248-8Search in Google Scholar

N. M. Bujurke, S. C. Shiralashetti, C. S. Salimath, An Application of Single Term Haar Wavelet Series in the Solution of non-linear oscillator Equations, Jour. Comp. Appl. Math. 227 (2010) 234-244.BujurkeN. M.ShiralashettiS. C.SalimathC. S.An Application of Single Term Haar Wavelet Series in the Solution of non-linear oscillator EquationsJour. Comp. Appl. Math227201023424410.1016/j.cam.2008.03.012Search in Google Scholar

N. M. Bujurke, S. C. Shiralashetti, C. S. Salimath, Computation of eigenvalues and solutions of regular Sturm-Liouville problems using Haar wavelets, Jour. Comp. Appl. Math. 219 (2008) 90-101.BujurkeN. M.ShiralashettiS. C.SalimathC. S.Computation of eigenvalues and solutions of regular Sturm-Liouville problems using Haar waveletsJour. Comp. Appl. Math21920089010110.1016/j.cam.2007.07.005Search in Google Scholar

S.C. Shiralashetti, L. M. Angadi, A. B. Deshi, M. H. Kantli, Haar wavelet method for the numerical solution of Klein?Gordan equations, Asian-European J. Math. 9(01) (2016) 1650012.ShiralashettiS.C.AngadiL. M.DeshiA. B.KantliM. H.Haar wavelet method for the numerical solution of Klein?Gordan equationsAsian-European J. Math9012016165001210.1142/S1793557116500121Search in Google Scholar

S.C. Shiralashetti, A.B. Deshi, An efficient haar wavelet collocation method for the numerical solution of multi-term fractional differential equations. Nonlinear Dyn. 83 (2016) 293-303.ShiralashettiS.C.DeshiA.B.An efficient haar wavelet collocation method for the numerical solution of multi-term fractional differential equationsNonlinear Dyn83201629330310.1007/s11071-015-2326-4Search in Google Scholar

S.C. Shiralashetti, A. B. Deshi, P. B Mutalik Desai, Haar wavelet collocation method for the numerical solution of singular initial value problems, Ain Shams Eng. J. 7(2) (2016) 663-670.ShiralashettiS.C.DeshiA. B.P. B Mutalik Desai, Haar wavelet collocation method for the numerical solution of singular initial value problemsAin Shams Eng. J72201666367010.1016/j.asej.2015.06.006Search in Google Scholar

S.C. Shiralashetti, A.B. Deshi, Haar Wavelet Collocation Method for Solving Riccati and Fractional Riccati Differential Equations, Bulletin. Math. Sci. Appl. 17 (2016) 46-56.ShiralashettiS.C.DeshiA.B.Haar Wavelet Collocation Method for Solving Riccati and Fractional Riccati Differential Equations, BulletinMath. Sci. Appl172016465610.18052/www.scipress.com/BMSA.17.46Search in Google Scholar

S.C. Shiralashetti, L. M. Angadi, M. H. Kantli, A. B. Deshi, Numerical solution of parabolic partial differential equations using adaptive gird Haar wavelet collocation method, Asian-European J. Math. (2016), 1750-026.ShiralashettiS.C.AngadiL. M.KantliM. H.DeshiA. B.Numerical solution of parabolic partial differential equations using adaptive gird Haar wavelet collocation methodAsian-European J. Math2016175002610.1142/S1793557117500267Search in Google Scholar

S.C. Shiralashetti, R. A. Mundewadi, Leibnitz-Haar Wavelet Collocation Method for the Numerical Solution of Nonlinear Fredholm Integral Equations. Inter. J. Eng. Sci. Res. Tech. 5(9) (2016) 264-273.ShiralashettiS.C.MundewadiR. A.Leibnitz-Haar Wavelet Collocation Method for the Numerical Solution of Nonlinear Fredholm Integral EquationsInter. J. Eng. Sci. Res. Tech592016264273Search in Google Scholar

M. H. Reihani, Z. Abadi, Rationalized Haar functions method for solving Fredholm and Volterra integral equations, J. Comp. Appl. Math. 200 (2007) 12?20.ReihaniM. H.AbadiZ.Rationalized Haar functions method for solving Fredholm and Volterra integral equationsJ. Comp. Appl. Math200200712?2010.1016/j.cam.2005.12.026Search in Google Scholar

V. Mishra, H. Kaur and R. C. Mittal. Haar wavelet algorithm for solving certain differential, integral and integro-differential equations. Int. J. of Appl. Math. Mech., 8 (6) (2012): 69-82.MishraV.KaurH.MittaR. C.Haar wavelet algorithm for solving certain differential, integral and integro-differential equationsInt. J. of Appl. Math. Mech8620126982Search in Google Scholar

H. Wiener, Structural determination of paraffin boiling points, J. Amer. Chem. Soc. 69 (1947) 17-20.WienerH.Structural determination of paraffin boiling pointsJ. Amer. Chem. Soc691947172010.1021/ja01193a005Search in Google Scholar

I. Gutman, Relation between hyper–Wiener and Wiener index, Chem. Phys. Lett. 364 (2002) 352-356.GutmanI.Relation between hyper–Wiener and Wiener indexChem. Phys. Lett364200235235610.1016/S0009-2614(02)01343-XSearch in Google Scholar

D. J. Klein, I. Lukovits, I. Gutman, On the definition of the hyper–Wiener index for cycle–containing structures J. Chem. Inf. Comput. Sci. 35 (1995) 50-52.KleinD. J.LukovitsI.GutmanI.On the definition of the hyper–Wiener index for cycle–containing structuresJ. Chem. Inf. Comput Sci351995505210.1021/ci00023a007Search in Google Scholar

D. Plavšić, S. Nikolić, N. Trinajstić, Z. Mihalić, On the Harary index for the characterization of chemical graphs, J. Math. Chem. 12 (1993) 235-250.PlavšićD.NikolićS.TrinajstićN.MihalićZ.On the Harary index for the characterization of chemical graphsJ. Math. Chem12199323525010.1007/BF01164638Search in Google Scholar

I. Gutman, A. A. Dobrynin, S. Klavžar, L. Pavlović,Wiener–type invariants of trees and their relation, Bull. Inst. Comb. Appl. 40 (2004) 23-30.GutmanI.DobryninA. A.KlavžarS.PavlovićL.Wiener–type invariants of trees and their relationBull. Inst. Comb. Appl4020042330Search in Google Scholar

D. J. Klein, I. Gutman, Wiener–number–related sequences, J. Chem. Inf. Comput. Sci. 39 (1999) 534-536.KleinD. J.GutmanI.Wiener–number–related sequencesJ. Chem. Inf. Comput. Sci39199953453610.1021/ci980133sSearch in Google Scholar

H. Hosoya, On some counting polynomials in chemistry, Discrete Applied Mathematics, 19 (1-3)(1988) 239-257.HosoyaH.On some counting polynomials in chemistry, Discrete Applied Mathematics191-3198823925710.1016/0166-218X(88)90017-0Search in Google Scholar

E. V. Konstantinova, M. V. Diudea, The Wiener polynomial derivatives and other topological indices in chemical research Croat. Chem. Acta 73 (2000) 383-403.KonstantinovaE. V.DiudeaM. V.The Wiener polynomial derivatives and other topological indices in chemical researchCroat. ChemActa732000383403Search in Google Scholar

G. Cash, S. Klavžar, M. Petkovšek, Three methods for calculation of the hyper–Wiener index of molecular graphs J. Chem. Inf. Comput. Sci. 43 (2002) 571-576.CashG.KlavžarS.PetkovšekM.Three methods for calculation of the hyper–Wiener index of molecular graphsJ. Chem. Inf. Comput. Sci43200257157610.1021/ci010099912086516Search in Google Scholar

I. Gutman, Hosoya polynomial and the distance of the total graph of a tree, Publ. Elektrotehn. Fak. (Beograd) Ser. Mat., 10 (1999) 53-58.GutmanI.Hosoya polynomial and the distance of the total graph of a tree, Publ. ElektrotehnFak. (Beograd) Ser. Mat1019995358Search in Google Scholar

I. Gutman, S. Klavžar, M. Petkovšek, P. Žigert, On Hosoya polynomials of benzenoid graphs, MATCH Commun. Math. Comput. Chem., 43 (2001) 49-66.GutmanI.KlavžarS.PetkovšekM.ŽigertP.On Hosoya polynomials of benzenoid graphs, MATCH CommunMath. Comput. Chem4320014966Search in Google Scholar

M. Lepović, I. Gutman, A collective property of trees and chemical trees, J. Chem. Inf. Comput. Sci., 38 (1998) 823-826.LepovićM.GutmanI.A collective property of trees and chemical treesJ. Chem. Inf. Comput. Sci38199882382610.1021/ci980004bSearch in Google Scholar

K. P. Narayankar, S. B. Lokesh, V. Mathad, I. Gutman, Hosoya polynomial of Hanoi graphs, Kragujevac J. Math., 36 (2012) 51-57.NarayankarK. P.LokeshS. B.MathadV.GutmanI.Hosoya polynomial of Hanoi graphsKragujevac J. Math3620125157Search in Google Scholar

H. S. Ramane, K. P. Narayankar, S. S. Shirkol, A. B. Ganagi, Terminal Wiener index of line graphs, MATCH Commun. Math. Comput. Chem., 69 (2013) 775-782.RamaneH. S.NarayankarK. P.ShirkolS. S.GanagiA. B.Terminal Wiener index of line graphs, MATCH CommunMath. Comput. Chem69201377578210.1155/2013/857908Search in Google Scholar

H. S. Ramane, S.C. Shiralashetti, R. A. Mundewadi, R. B. Jummannaver, Numerical Solution of Fredholm Integral Equations Using Hosoya Polynomial of Path Graphs, American Journal of Numerical Analysis, 2017, Vol. 5, No. 1, 11-15.RamaneH. S.ShiralashettiS.C.MundewadiR. A.JummannaverR. B.Numerical Solution of Fredholm Integral Equations Using Hosoya Polynomial of Path GraphsAmerican Journal of Numerical Analysis201711115Search in Google Scholar

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