Solution of Nonlinear Fredholm-Volterra Integral Equations via Block-Pulse Functions
الموضوعات : مجله بین المللی ریاضیات صنعتی
1 - Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran.
2 - Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran.
الکلمات المفتاحية: Block-pulse functions, Nonlinear Fredholm-Volterra integral equation, Operational matrices,
ملخص المقالة :
In this paper, a new simple direct method to solve nonlinear Fredholm-Volterra integral equations is presented. By using Block-pulse (BP) functions, their operational matrices and Taylor expansion a nonlinear Fredholm-Volterra integral equation converts to a nonlinear system. Some numerical examples illustrate accuracy and reliability of our solutions. Also, effect of noise shows our solutions are stable.
[1] L. M. Delves, J. Walsh, Numerical solution of integral equations, Clarendon Press, Oxford (1974).
[2] L. M. Delves, J. L. Mohamed, Computational methods for integral equations, Cambridge University Press, (1985).
[3] M. A. Golberg, Numerical solution of integral equations, Plenum Press, (1990).
[4] K. E. Atkinson, the Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, (1997).
[5] P. J. Collins, Differential and integral equations, Oxford University Press, (2006).
[6] M. Rahman, Integral Equations and Their Applications, WIT Press, (2007).
[7] A. Wazwaz, Linear and nonlinear integral equations methods and applications, Higher Education Press, Beijing and SpringerVerlag Berlin Heidelberg, (2011).
[8] E. Babolian, T. Lotfi, M. Paripour, Wavelet moment method for solving Fredholm integral equations of the first kind, Applied Mathematics and Computation 186 (2007) 1467-1471.
[9] K. Maleknejad, T. Lotfi, K. Mahdiani, Numerical solution of first kind Fredholm integral equations with wavelets-Galerkin method (WGM) and wavelets precondition, Applied Mathematics and Computation 186 (2007) 794-800.
[10] E. Babolian, Z. Masouri, Direct method to solve Volterra integral equation of the first kind using operational matrix with blockpulse functions, Journal of Computational and Applied Mathematics 220 (2008) 51-57.
[11] Z. Masouri, E. Babolian, S. H. Varmazyar, An expansion iterative method for numerically solving Volterra integral equation of the first kind, Computers and Mathematics with Applications 59 (2010), 1491-1499.
[12] E. Babolian, Z. Masouri, S. H. Varmazyar, Numerical solution of nonlinear VolterraFredholm integro-differential equations via direct method using triangular functions, Computers and Mathematics with Applications 58 (2009). 239-247
[13] A. Shahsavaran, Numerical Solution of Nonlinear Fredholm-Volterra Integral Equations via Piecewise Constant Function by Collocation Method, American Journal of Computational Mathematics 1 (2011) 134-138.
[14] M. Zarebnia, A numerical solution of nonlinear Volterra-Fredholm integral equations, Journal of Applied Analysis and Computation Volume 3 ( 2013) 95-104.
[15] Y. Ordokhani, M. Razzaghi, Solution of nonlinear Volterra Fredholm Hammerstein integral equations via a collocation method and rationalized Haar functions, Applied Mathematics Letters 21 ( 2008) 4-9.
[16] E. Kreyszig, Introduction Functional Analysis with Applications, John Wiley and Sons Incorporated, 1978.
