Solution of Nonlinear Fredholm-Volterra Integral Equations via Block-Pulse Functions
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
F. Abbasi
1
(Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran.)
M. Mohamadi
2
(Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran.)
کلید واژه: Block-pulse functions, Nonlinear Fredholm-Volterra integral equation, Operational matrices,
چکیده مقاله :
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.
در این تحقیق روشی مستقیم در حل معادلات انتگرال فردهلم-ولترا غیرخطی ارائه می کنیم. با بکارگیری توابع بلک پالس و ماتریسهای عملیاتی و همچنین بسط تیلور معادله را به یک دستگاه غیرخطی تبدیل می‌کنیم. با چند مثال عددی دقت و کارایی روش را نشان می‌دهیم.
[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.
