Abstract
The integral equations can be classified in the following way
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References
Abbas, Z., Vahdati, S., Atan, K., Long, N.: Legendre multi-wavelets direct method for linear integro-differential equations. Appl. Math. Sci. 3, 693–700 (2006)
Atkinson, K.E.: The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press, Cambridge (1997)
Aziz, I.: Siraj-ul-Islam: New algorithms for the numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets. J. Comput. Appl. Math. 239, 333–345 (2013)
Babolian, E., Bazm, S., Lima, P.: Numerical solution of nonlinear two-dimensional integral equations using rationalized Haar functions. Commun. Nonlinear Sci. Numer. Simul. 16, 1164–1175 (2011)
Babolian, E., Maleknejad, K., Mordad, M., Rahimi, B.: A numerical method for solving FredholmVolterra integral equations in two-dimensional spaces using Block Pulse functions and an operational matrix. J. Comput. Appl. Math. 235, 3965–3971 (2011)
Babolian, E., Shahsavaran, A.: Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets. J. Comput. Appl. Math. 225, 87–95 (2009)
Biazar, J., Ebrahimi, H.: Chebyshev wavelets approach for nonlinear systems of Volterra integral equations. Comput. Math. Appl. 63, 608–616 (2012)
Cattani, C.: Shannon wavelets for the solution of integro-differential equations. Mathematical Problems in Engineering 2010 (2010). doi: 10.1155/2010/408418
Cattani, C., Kudreyko, A.: Harmonic wavelet method towards solution of the Fredholm type integral equations of the second kind. Appl. Math. Comput. 215, 4164–4171 (2010)
El-Sayed, S., Abdel-Aziz, M.: A comparison of Adomian’s decomposition method and wavelet-Galerkin method for solving integro-differential equations. Appl. Math. Comput. 136, 151–159 (2003)
Ghasemi, M., Kajani, M.: Numerical solution of time-varying delay systems by Chebyshev wavelets. Appl. Math. Model. 35, 5235–5244 (2011)
Hsiao, C.: Hybrid function method for solving Fredholm and Volterra integral equations of the second kind. Comp. Appl. Math. 230, 59–68 (2009)
Hsiao, C., Chen, C.: Solving integral equations via Walsh functions. Comput. Electr. Eng. 6, 279–292 (1979)
Khellat, F., Yousefi, S.: The linear Legendre mother wavelets operational matrix of integration and its application. J. Franklin Inst. 343, 181–190 (2006)
Lepik, Ü.: Haar wavelet method for nonlinear integro-differential equations. Appl. Math. Comp. 176, 324–333 (2006)
Lepik, Ü.: Application of the Haar wavelet transform to solving integral and differential equations. Proc. Estonian Acad. Sci. Phys. Math. 56, 28–46 (2007)
Lepik, Ü.: Solving differential and integral equations by the Haar wavelet method; revisited. Int. J. Math. Comput. 1, 43–52 (2008)
Lepik, Ü.: Solving integral and differential equations by the aid of nonuniform Haar wavelets. Appl. Math. Comp. 198, 326–332 (2008)
Lepik, Ü., Tamme, E.: Application of Haar wavelets for solution of linear integral equations. In: H. Akca, A. Boucherif, V. Covachev (eds.) Dynamical Systems and Applications, pp. 494–507 (2005)
Lepik, Ü., Tamme, E.: Solution of nonlinear Fredholm integral equations via the Haar wavelet method. Proc. Estonian Acad. Sci. Phys. Math. 56, 17–27 (2007)
Maleknejad, K., Karami, M.: Numerical solution of non-linear Fredholm integral equations by using multiwavelets in the Petrov-Galerkin method. Appl. Math. Comput. 168, 102–110 (2005)
Maleknejad, K., Lotfi, T., Rostami, Y.: Numerical computational method in solving Fredholm integral equations of the second kind by using Coifman wavelet. Appl. Math. Comput. 186, 212–218 (2007)
Maleknejad, K., Mirzaee, B.: Using rationalized Haar wavelet for solving linear integral equations. Appl. Math. Comp. 160, 579–589 (2005)
Maleknejad, K., Mirzaee, F.: Numerical solution of linear Fredholm integral equations system by rationalized Haar functions method. Int. J. Comput. Math. 80, 1397–1405 (2003)
Maleknejad, K., Mirzaee, F., Abbasbandy, S.: Solving linear integro-differential equations system by using rationalized Haar functions method. Appl. Math. Comput. 155, 317–328 (2004)
Maleknejad, K., Mollapourasl, R., Alizadeh, M.: Numerical solution of Volterra type integral equation of the first kind with wavelet basis. Appl. Math. Comput. 194, 400–405 (2007)
Maleknejad, K., Rahimi, B.: Modification of Block Pulse functions and their application to solve numerically Volterra integral equation of the first kind. Commun. Nonlinear Sci. Numer. Simul. 16, 2469–2477 (2011)
Maleknejad, K., Shahrezaee, M., Khatami, H.: Numerical solution of integral equations system of the second kind by BlockPulse functions. Appl. Math. Comput. 166, 15–24 (2005)
Maleknejad, K., Sohrabi, S.: Numerical solution of Fredholm integral equations of the first kind by using Legendre wavelets. Appl. Math. Comput. 186, 836–843 (2007)
Maleknejad, K., Sohrabi, S., Baranji, B.: Application of 2D-BPFs to nonlinear integral equations. Commun. Nonlinear Sci. Numer. Simul. 15, 527–535 (2010)
Mirzaee, F.: Numerical computational solution of the linear Volterra integral equations system via rationalized Haar functions. J. King Saud Univ. Sci. 22, 265–268 (2010)
Mirzaee, F., Hadadiyan, E.: Approximate solutions for mixed nonlinear Volterra-Fredholm type integral equations via modified Block-Pulse functions. J. Assoc. Arab Univ. Basic Appl. Sci. 12, 65–73 (2012)
Ordokhani, Y.: Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via rationalized Haar functions. Appl. Math. Comput. 180, 436–443 (2006)
Rabbani, M., Maleknejad, K., Aghazadeh, N., Mollapourasl, R.: Computational projection methods for solving Fredholm integral equation. Appl. Math. Comput. 191, 140–143 (2007)
Reihani, M., Abadi, Z.: Rationalized Haar functions method for solving Fredholm and Volterra integral equations. J. Comput. Appl. Math. 200, 12–20 (2007)
Sepehrian, B., Razzaghi, M.: Single-term Walsh series method for the Volterra integro-differential equations. Eng. Anal. Bound. Elem. 28, 1315–1319 (2004)
Shahsavaran, A., Shahsavaran, A.: Properties of BPFs for approximating the solution of nonlinear Fredholm integro differential equation. Appl. Math. Sci. 6, 1563–1569 (2012)
Shang, X., Han, D.: Numerical solution of Fredholm integral equations of the first kind by using linear Legendre multi-wavelets. Appl. Math. Comput. 191, 440–444 (2007)
Sloss, B., Blyth, W.: A Walsh function method for a non-linear Volterra integral equation. J. Franklin Inst. 340, 25–41 (2003)
Sohrabi, S.: Comparison Chebyshev wavelets method with BPFs method for solving Abel’s integral equation. Ain Shams Eng. J. 2, 249–254 (2011)
Xiao, J., Wen, L., Zhang, D.: Solving second kind Fredholm integral equation by periodic wavelet Galerkin method. Appl. Math. Comput. 175, 508–518 (2006)
Yousefi, S.: Numerical solution of Abel’s integral equation by using Legendre wavelets. Appl. Math. Comput. 175, 574–580 (2006)
Yousefi, S., Razzaghi, M.: Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations. Math. Comput. Simul. 70, 1–8 (2005)
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Lepik, Ü., Hein, H. (2014). Integral Equations. In: Haar Wavelets. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-04295-4_5
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