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Numerical solutions of fuzzy nonlinear integral equations of the second kind | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 8، دوره 11، شماره 1، اردیبهشت 2014، صفحه 135-145 اصل مقاله (136.19 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2014.1399 | ||
| نویسندگان | ||
| M. Otadi* ؛ M. Mosleh | ||
| Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer- sity, Firoozkooh, Iran | ||
| چکیده | ||
| In this paper, we use the parametric form of fuzzy numbers, and an iterative approach for obtaining approximate solution for a class of fuzzy nonlinear Fredholm integral equations of the second kind is proposed. This paper presents a method based on Newton-Cotes methods with positive coefficient. Then we obtain approximate solution of the fuzzy nonlinear integral equations by an iterative approach. | ||
| کلیدواژهها | ||
| Fuzzy nonlinear Fredholm integral equations؛ Newton-Cotes methods؛ Parametric form of a fuzzy number | ||
| مراجع | ||
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\bibitem{aba} S. Abbasbandy, E. Babolian and M. Alavi, {\it Numerical method for solving linear fredholm fuzzy integral equations of the second kind}, Chaos Solitons \& Fractals, {\bf 31} (2007), 138-146. \bibitem{al1} T. Allahviranloo and M. Otadi, {\it Gaussian quadratures for approximate of fuzzy integrals}, Applied Mathematics and Computation, {\bf 170} (2005), 874-885. \bibitem{al2} T. Allahviranloo and M. Otadi, {\it Gaussian quadratures for approximate of fuzzy multiple integrals}, Applied Mathematics and Computation, {\bf 172} (2006), 175-187. \bibitem{at} K. E. Atkinson, {\it An introduction to numerical analysis}, New York: Wiley, 1987. \bibitem{bsa} E. Babolian, H. S. Goghary and S. Abbasbandy, {\it Numerical solution of linear fredholm fuzzy integral equations of the second kind by Adomian method}, Applied Mathematics and Computation, {\bf 161} (2005), 733-744. \bibitem{baker} C. T. H. Baker, {\it A perspective on the numerical treatment of volterra equations}, Journal of Computational and Appllied Mathematics, {\bf 125} (2000), 217-249. \bibitem{bgggp} M. I. Berenguer, D. Gamez, A. I. Garralda-Guillem, M. Ruiz Galan and M. C. Serrano Perez, {\it Biorthogonal systems for solving volterra integral equation systems of the second kind}, Journal of Computational and Appllied Mathematics, {\bf 235} (2011), 1875-1883. \bibitem{b} A. M. Bica, {\it Error estimation in the approximation of the solution of nonlinear fuzzy fredholm integral equations}, Information Sciences, {\bf 178} (2008), 1279-1292. \bibitem{bf} A. H. Borzabadi and O. S. Fard, {\it A numerical scheme for a class of nonlinear fredholm integral equations of the second kind}, Journal of Computational and Applied Mathematics, {\bf 232} (2009), 449-454. \bibitem{cz} S. S. L. Chang and L. Zadeh, {\it On fuzzy mapping and control}, IEEE Trans. System Man Cybernet, {\bf 2} (1972), 30-34. \bibitem{ct} Y. Chen and T. Tang, {\it Spectral methods for weakly singular volterra integral equations with smooth solutions}, Journal of Computational and Appllied Mathematics, {\bf 233} (2009), 938-950. \bibitem{cm} W. Congxin and M. Ming, {\it On embedding problem of fuzzy number spaces}, Part 1, Fuzzy Sets and Systems, {\bf 44} (1991), 33-38. \bibitem{dd} D. Dubois and H. Prade, {\it Operations on fuzzy numbers}, International Journal of Systems Science, {\bf 9} (1978), 613-626.
\bibitem{dp} D. Dubois and H. Prade, {\it Towards fuzzy differential calculus}, Fuzzy Sets and Systems, {\bf 8} (1982), 1-7. \bibitem{ez} R. Ezzati and S. Ziari, {\it Numerical solution and error estimation of fuzzy fredholm integral equation using fuzzy bernstein polynomials}, Australian Journal of Basic and Applied Sciences, {\bf 5} (2011), 2072-2082.
\bibitem{fp} M. A. Fariborzi Araghi and N. Parandin, {\it Numerical solution of fuzzy fredholm integral equations by the lagrange interpolation based on the extension principle}, Soft Computing, {\bf 15} (2011), 2449-2456. \bibitem{fmk} M. Friedman, M. Ma and A. Kandel, {\it Numerical solutions of fuzzy differential and integral equations}, Fuzzy Sets and Systems, {\bf 106} (1999), 35-48. \bibitem{fmk2} M. Friedman, M. Ma and A. Kandel, {\it Solution to the fuzzy integral equations with arbitrary kernels}, International Journal of Approximate Reasoning, {\bf 20} (1999), 249-262. \bibitem{gv} R. Goetschel and W. Vaxman, {\it Elementary fuzzy calculus}, Fuzzy Sets and Systems, {\bf 18} (1986), 31-43. \bibitem{h} H. Hochstadt, {\it Integral equations}, New York: Wiley, 1973. \bibitem{kg} A. Kaufmann and M. M. Gupta, {\it Introduction fuzzy arithmetic}, Van Nostrand Reinhold, New York, 1985. \bibitem{kal}O. Kaleva, {\it Fuzzy differential equations}, Fuzzy Sets and Systems, {\bf 24} (1987), 301-317. \bibitem{kauthen} J. P. Kauthen, {\it Continuous time collocation method for volterra-fredholm integral equations}, Numerische Math., {\bf 56} (1989), 409-424. \bibitem{kcy} G. J. Klir, U. S. Clair and B. Yuan, {\it Fuzzy set theory: foundations and applications}, Prentice-Hall, 1997. \bibitem{linz} P. Linz, {\it Analytical and numerical methods for volterra equations}, SIAM, Philadelphia, PA, 1985. \bibitem{mfk} M. Ma, M. Friedman and A. Kandel, {\it A new fuzzy arithmetic}, Fuzzy Sets and Systems, {\bf 108} (1999), 83-90. \bibitem{mola} A. Molabahrami, A. Shidfar and A. Ghyasi, {\it An analytical method for solving linear fredholm fuzzy integral equations of the second kind}, Computers \& Mathematics with Applications, {\bf 61} (2011), 2754-2761.
\bibitem{mo11} M. Mosleh and M. Otadi, {\it Numerical solution of fuzzy integral equations using Bernstein polynomials}, Australian Journal of Basic Applied Sciences, {\bf 5} (2011), 724-728.
\bibitem{pf1} N. Parandin and M. A. Fariborzi Araghi, {\it The approximate solution of linear fuzzy fredholm integral equations of the second kind by using iterative interpolation}, World Academy of Science, Engineering and Technology, {\bf 49} (2009), 947-984.
\bibitem{pf2} N. Parandin and M. A. Fariborzi Araghi, {\it The numerical solution of linear fuzzy fredholm integral equations of the second kind by using finite and divided differences methods}, Soft Computing, {\bf 15} (2010), 729-741.
\bibitem{pr} M. L. Puri and D. Ralescu, {\it Fuzzy random variables}, Journal of Mathematical Analysis and Applications, {\bf 114} (1986), 409-422. \bibitem{fard} O. Solaymani Fard and M. Sanchooli, {\it Two successive schemes for numerical solution of linear fuzzy fredholm integral equations of the second kind}, Australian Journal of Basic Applied Sciences, {\bf 4} (2010), 817-825.
\bibitem{sy} H. H. Sorkun and S. Yalcinbas, {\it Approximate solutions of linear volterra integral equation systems with variable coefficients}, Applied Mathematical Modelling, {\bf 34} (2010), 3451-3464. \bibitem{sb} J. Stoer and R. Bulirsch, {\it Introduction to numerical analysis}, Springer-Verlag,New York, 1993. \bibitem{laz} L. A. Zadeh, {\it The concept of a linguistic variable and its application to approximate reasoning}, Information Sciences, {\bf 8} (1975), 199-249. | ||
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