{"title":"Spline Collocation for Solving System of Fredholm and Volterra Integral Equations","authors":"N. Ebrahimi, J. Rashidinia","volume":90,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1008,"pagesEnd":1013,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9999855","abstract":"
In this paper, numerical solution of system of
\r\nFredholm and Volterra integral equations by means of the Spline
\r\ncollocation method is considered. This approximation reduces the
\r\nsystem of integral equations to an explicit system of algebraic
\r\nequations. The solution is collocated by cubic B-spline and the
\r\nintegrand is approximated by the Newton-Cotes formula. The error
\r\nanalysis of proposed numerical method is studied theoretically. The
\r\nresults are compared with the results obtained by other methods to
\r\nillustrate the accuracy and the implementation of our method.<\/p>\r\n","references":"[1] Atkinson,K. E: The Numerical Solution of Integral Equations of the\r\nSecond Kind, Cambridge University Press, New York, (1997).\r\n[2] Delves,L. M , Mohammed,J. L: Computational Methods for Integral\r\nEquations , Cambridge University Press, Cambridge, (1985).\r\n[3] Saeed,R. K , Ahmed,C. S: Approximate Solution for the System of Nonlinear\r\nVolterra Integral Equations of the Second Kind by using Blockby-\r\nblock Method,Australian Journal of Basic and Applied Sciences,\r\n2(1), ,114-124(2008).\r\n[4] Babolian,E , Masouri,Z, Hatamzadeh-Varmazyar,S: A Direct Method\r\nfor Numerically Solving Integral Equations System Using Orthogonal\r\nTriangular Functions, Int. J. 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