Maleknejad, K.; Mirzaee, F.; Abbasbandy, S. Solving linear integro-differential equations system by using rationalized Haar functions method. (English) Zbl 1056.65144 Appl. Math. Comput. 155, No. 2, 317-328 (2004). Summary: We use rationalized Haar functions to estimate the solution of a system of linear integro-differential equations. Properties of rationalized Haar functions are first presented, and the operational matrix of the product of two rationalized Haar function vectors is utilized to reduce the computation of the linear integro-differential equations system to some algebraic equations. By using numerical examples we show our estimation have a good degree of accuracy. Cited in 40 Documents MSC: 65R20 Numerical methods for integral equations 45J05 Integro-ordinary differential equations 45R05 Random integral equations 65T60 Numerical methods for wavelets Keywords:linear integro-differential equations system; operational matrix; product operation; rationalized Haar functions; numerical examples PDFBibTeX XMLCite \textit{K. Maleknejad} et al., Appl. Math. Comput. 155, No. 2, 317--328 (2004; Zbl 1056.65144) Full Text: DOI References: [1] Delves, L. M.; Mohammad, J. L., Computational Method for Integral Equations (1983), Cambridge university Press [2] R.T. Lynch, J.J. Reis, Haar transform image coding, in: Proc. National Telecommum. Conf., Dallas, TX, 1976, pp. 44.3-1-44.3; R.T. Lynch, J.J. Reis, Haar transform image coding, in: Proc. National Telecommum. Conf., Dallas, TX, 1976, pp. 44.3-1-44.3 [3] K.G. Beauchamp, Walsh function and their application, 1975; K.G. Beauchamp, Walsh function and their application, 1975 · Zbl 0326.42007 [4] K. Maleknejad, F. Mirzaee, Numerical solution of integro-differential equations by using rationalized Haar functions method, Kybernetes, Int. J. Syst. Math., in press; K. Maleknejad, F. Mirzaee, Numerical solution of integro-differential equations by using rationalized Haar functions method, Kybernetes, Int. J. Syst. Math., in press · Zbl 1160.45303 [5] K. Maleknejad, F. Mirzaee, Numerical solution of linear Fredholm integral equations system by rationalized Haar functions method, Int. J. Comput. Math., in press; K. Maleknejad, F. Mirzaee, Numerical solution of linear Fredholm integral equations system by rationalized Haar functions method, Int. J. Comput. Math., in press · Zbl 1045.65115 [6] Ohkita, M.; Kobayashi, Y., An application of rationalized Haar functions to solution of linear differential equations, IEEE Trans. Circuit Syst., 9, 853-862 (1986) · Zbl 0613.65072 [7] Ohkita, M.; Kobayashi, Y., An application of rationalized Haar functions to solution of linear partial differential equations, Math. Comput. Simulat., 30, 419-428 (1988) · Zbl 0659.65109 [8] M. Razzaghi, J. Nazarzadeh, Walsh functions, Wiley Encyclopedia of Electrical and Electronics Engineering, vol. 23, 1999, pp. 429-440; M. Razzaghi, J. Nazarzadeh, Walsh functions, Wiley Encyclopedia of Electrical and Electronics Engineering, vol. 23, 1999, pp. 429-440 [9] J.J. Reis, R.T. Lynch, J. Butman, Adaptive Haar transform video bandwidth reduction system for RPV’s, in: Proc. Ann. Meeting Soc. Photo Optic Inst. Eng. (SPIE), San Diego, CA, 1976, pp. 24-35; J.J. Reis, R.T. Lynch, J. Butman, Adaptive Haar transform video bandwidth reduction system for RPV’s, in: Proc. Ann. Meeting Soc. Photo Optic Inst. Eng. (SPIE), San Diego, CA, 1976, pp. 24-35 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.