Lakestani, Mehrdad; Dehghan, Mehdi Numerical solution of fourth-order integro-differential equations using Chebyshev cardinal functions. (English) Zbl 1191.65183 Int. J. Comput. Math. 87, No. 6, 1389-1394 (2010). Summary: A numerical technique is presented for the solution of fourth-order integro-differential equations. This method uses the Chebyshev cardinal functions. The method consists of expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the operational matrix of derivative, we reduce the problem to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces very accurate results. Cited in 14 Documents MSC: 65R20 Numerical methods for integral equations 45J05 Integro-ordinary differential equations 45G10 Other nonlinear integral equations Keywords:nonlinear two-point boundary value problem; Chebyshev cardinal functions; operational matrix of derivative; fourth-order integro-differential equations; numerical examples PDF BibTeX XML Cite \textit{M. Lakestani} and \textit{M. Dehghan}, Int. J. Comput. Math. 87, No. 6, 1389--1394 (2010; Zbl 1191.65183) Full Text: DOI References: [1] DOI: 10.1016/0362-546X(83)90070-6 · Zbl 0505.45002 · doi:10.1016/0362-546X(83)90070-6 [2] Agarwal R. P., Boundary Value Problems for High Ordinary Differential Equations (1986) [3] Boyd J. P., Chebyshev and Fourier Spectral Methods, 2. ed. (2001) · Zbl 0994.65128 [4] DOI: 10.1080/00207160500069847 · Zbl 1087.65119 · doi:10.1080/00207160500069847 [5] DOI: 10.1080/00207160701405436 · Zbl 1131.65107 · doi:10.1080/00207160701405436 [6] DOI: 10.2528/PIER07090403 · doi:10.2528/PIER07090403 [7] Dehghan M., Commun. Numer. Methods Eng. (2008) [8] DOI: 10.1016/j.cam.2005.05.034 · Zbl 1093.65122 · doi:10.1016/j.cam.2005.05.034 [9] DOI: 10.1007/978-1-4612-0101-4 · doi:10.1007/978-1-4612-0101-4 [10] DOI: 10.1016/j.mcm.2007.11.012 · Zbl 1156.92332 · doi:10.1016/j.mcm.2007.11.012 [11] DOI: 10.1007/s00607-008-0009-4 · Zbl 1154.65098 · doi:10.1007/s00607-008-0009-4 [12] DOI: 10.1016/j.camwa.2006.12.055 · Zbl 1141.65399 · doi:10.1016/j.camwa.2006.12.055 [13] Wazwaz A. M., A First Course in Integral Equations (1997) · Zbl 0924.45001 [14] DOI: 10.1016/S0096-3003(99)00225-8 · Zbl 1023.65150 · doi:10.1016/S0096-3003(99)00225-8 [15] DOI: 10.1016/j.amc.2006.03.023 · Zbl 1105.65128 · doi:10.1016/j.amc.2006.03.023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.