Abstract
A method for solving the nonlinear second-order Fredholm
integro-differential equations is presented. The approach is based
on a compactly supported linear semiorthogonal
A method for solving the nonlinear second-order Fredholm
integro-differential equations is presented. The approach is based
on a compactly supported linear semiorthogonal
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, vol. 45, no. 2, pp. 218–228, 2003.
View at: Publisher Site | Google ScholarA. Ayad, “Spline approximation for first order Fredholm integro-differential equations,” Universitatis Babeş-Bolyai. Studia. Mathematica, vol. 41, no. 3, pp. 1–8, 1996.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. H. Behiry and H. Hashish, “Wavelet methods for the numerical solution of Fredholm integro-differential equations,” International Journal of Applied Mathematics, vol. 11, no. 1, pp. 27–35, 2002.
View at: Google Scholar | Zentralblatt MATH | MathSciNetC. K. Chui, An Introduction to Wavelets, vol. 1 of Wavelet Analysis and Its Applications, Academic Press, Massachusetts, 1992.
View at: Zentralblatt MATH | MathSciNetJ. C. Goswami, A. K. Chan, and C. K. Chui, “On solving first-kind integral equations using wavelets on a bounded interval,” IEEE Transactions on Antennas and Propagation, vol. 43, no. 6, pp. 614–622, 1995.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. Lakestani, M. Razzaghi, and M. Dehghan, “Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets,” Mathematical Problems in Engineering, vol. 2005, no. 1, pp. 113–121, 2005.
View at: Publisher Site | Google ScholarP. Linz, “A method for the approximate solution of linear integro-differential equations,” SIAM Journal on Numerical Analysis, vol. 11, no. 1, pp. 137–144, 1974.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetG. Micula and G. Fairweather, “Direct numerical spline methods for first-order Fredholm integro-differential equations,” Revue d'Analyse Numérique et de Théorie de l'Approximation, vol. 22, no. 1, pp. 59–66, 1993.
View at: Google Scholar | Zentralblatt MATH | MathSciNetR. 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, vol. 45, no. 9, pp. 1332–1339, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetG. M. Phillips, “Analysis of numerical iterative methods for solving integral and integrodifferential equations,” The Computer Journal, vol. 13, no. 3, pp. 297–300, 1970.
View at: Publisher Site | Google Scholar | Zentralblatt MATHA. Ralston and P. Rabinowitz, A First Course in Numerical Analysis, McGraw-Hill, New York, 1985.
W. Volk, “The numerical solution of linear integro-differential equations by projection methods,” Journal of Integral Equations, vol. 9, no. 1, suppl., pp. 171–190, 1985.
View at: Google Scholar | Zentralblatt MATH | MathSciNet