Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices
In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions
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 K. Atkinson The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press 2, 1997.
 K. Maleknejad,S. Sohrabi and Y. Rostami Application of Wavelet Transform Analysis in Medical Frames Compression. Kybernetes, Int. J. Sys. Math, 37, 2, 343-351, 2008.
 A.M. Wazwaz Linear and nonlinear integral equations: Methods and applications. Higher Education, Springer, 2011.
 K. Maleknejad,R. Mollapourasl and M. Alizadeh, Numerical Solution of the Volterra Type Integral Equation of the First Kind with Wavelet Basis. Applied Mathematics and Computation , 194, 400-405, 2007.
 K. Maleknejad and M. Rabbani, A modification for solving Fredholm-Hammerstein integral equation by using wavelet basis. Kybernetes, Int. J. Sys. Math, 38, 615-620, 2009.
 K. Maleknejad and M. Nosrati Sahlan, The Method of Moments for Solution of Second Kind Fredholm Integral Equations Based on B-Spline Wavelets. International Journal of Computer Mathematics, Vol 87, No 7, 1602-1616, 2010.
 K. Maleknejad,R. Mollapourasl and M. shahabi, On solution of nonlinear integral equation based on fixed point technique and cubic B-spline scaling functions. Journal of Computational and Applied Mathematics, Volume 239, 346-358, 2013.
 K. Maleknejad,R. Mollapourasl and P. Mirzaei, Numerical solution of Volterra functional integral equation by using cubic B-spline scaling functions. Journal of Numerical Methods for Partial Differential Equations, 2013.
 K. Maleknejad,T. Lotfi and Y. Rostami, Numerical Computational Method in Solving Fredholm Integral Equations of the Second Kind by Using Coifman Wavelet. Applied Mathematics and Computation , 186, 212-218, 2007.
 C.K. Chui, An introduction to wavelets,Wavelet analysis and its applications. New york. Academic press, 1992.
 S.G. Mallat, A theory for multiresolution signal decomposition. The wavelet representation, IEEE Trans, Pattern Anal. Mach. Intell. vol 11, pp 674-693, 1989.
 E.A. Rawashdeh, Numerical solution of fractional integro-differential equations by collocation method. Applied Mathematics and Computation, vol 176, pp 1-6, 2006.
 N. Aghazadeh and K. Maleknejad Using quadratic B-spline scaling functions for solving integral equations. International Journal: Mathematical Manuscripts, No 1, 1-6, 2007.
 K. Koro and K. Abe Non-orthogonal spline wavelets for boundary element analysis. Engineering Analysis with Boundary Elements, 25, 149-164, 2001.
 M. Lakestani,M. Razzaghi and M. Dehghan Solution of nonlinear Fredholm- Hammerstein integral equations by using semiorthogonal spline wavelets. Mathematical Problems in Engineering, 113-121,
 M. Lakestani,M. Razzaghi and M. Dehghan Semiorthogonal spline wavelets approximation for Fredholm integro-differential equations. Mathematical Problems in Engineering, Article ID 96184, 12 pages, 2006.
 G. Ala,M.L. Di Silvestre , E. Francomano and A. Tortorici An advanced numerical model in solving thin-wire integral equations by using semi-orthogonal compactly supported spline wavelets. IEEE Transactions on Electromagnetic Compatibility 45 , No 2, 218-228, 2003.
 K. Maleknejad and M. Tavassoli Kajani Solving integro-differential equation by using hybrid Legendre and Block-Pulse functions. International Journal of Applied Mathematics, 11(1), 67-76, 2002.
 K. Maleknejad and Y. Mahmoudi Numerical solution of Integro-Differential Equation By Using Hybrid Taylor And Block-Pulse Functions. Far East Journal of Mathematical science , 9(2) 203-213, 2003.
 K. Maleknejad and T. Lotfi Method for Linear Integral Equations by Cardinal B-Spline Wavelet and Shannon Wavelet as Bases for Obtain Galerkin System. Applied Mathematics and Computation , 175, 347-355, 2006.
 K. Maleknejad,S. Sohrabi and Y. Rostami Numerical Solution of Nonlinear Volterra Integral Equations of the Second Kind by Using Chebyshev Polynomials. Applied Mathematics and Computation, 188, 123-128, 2007.
 K. Maleknejad,B. Basirat and E. Hashemizadeh Hybrid Legendre polynomials and Block-Pulse functions approach for nonlinear Volterra-Fredholm integro-differential equations. Computer and Mathematics with Application, Vol 61, 2821-2828, 2011.
 K. Maleknejad and M. Attary A Chebyshev collocation method for the solution of higher-order Fredholm-Volterra integro-differential equation system. U.P.B. Sci. Bull., Series A, Vol 74, Iss 4, 2012.
 A. Ayad Spline approximation for first order Fredholm integro-differential equations. Universitatis Babes-Bolyai. Studia. Mathematica 41 , No 3, 18 , 1996.
 G. Micula and G. Fairweather Direct numerical spline methods for first-order Fredholm integrodifferential equations. Revue dAnalyse Numerique et de Theorie de lApproximation 22 , No 1, 59-66, 1993.
 R.D. Nevels, J.C. Goswami and H. Tehrani Semi-orthogonal versus orthogonal wavelet basis sets for solving integral equations. IEEE Transactions on Antennas and Propagation 45 , No 9, 1332-1339,1997.
 M.A. Fariborzi Araghi,S. Daliri and M. Bahmanpour numerical solution of integro-differential equation by using chebyshev wavelet operational matrix of integration. international journal of mathematical modelling and computations, 02, 127-136, 2012.
 G. Ala,N.L. D Silvestre,E. Francomano and A. Tortorici An advanced numerical model in solving thin-wire integral equations by using semi-orthogonal compactly supported spline wavelets. IEEE Trans, Electromagn, Compat,1995
 B.K. Alpert Wavelets and other bases for fast numerical linear algebra, Wavelets: A Tutorial Theory and Applications. Wavelet Anal, Appl, vol 2, Academic Press, Massachusetts,181-216,1992.
 K. Mustapha A Petrov-Galerkin method for integro-differential equations with a memory term. Int. J. Open Problems Compt, 2008.
 J.C. Goswami,A.K. Chan and C.K. Chui On Solving First-Kind Integral Equations Using Wavelets on a Bounded Interval. IEEE Trance.Antennas propaget,43(6),614-622, 1995.