Rationalized Haar functions method for solving Fredholm and Volterra integral equations. (English) Zbl 1107.65122

Summary: The authors present a computational technique for Fredholm integral equation of the second kind and Volterra integral equation of the second kind. The method is based upon Haar functions approximation. Properties of rationalized Haar functions are first presented, the operational matrix of integration together with product operational matrix and Newton-Cotes nodes are utilized to reduce the computation of integral equations into some algebraic equations. The method is computationally attractive and applications are demonstrated through illustrative examples.


65R20 Numerical methods for integral equations
65T60 Numerical methods for wavelets
45B05 Fredholm integral equations
45D05 Volterra integral equations
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[1] K.G. Beauchamp, Walsh Functions and their Applications, 1975. · Zbl 0326.42007
[2] Blyth, W.F.; May, R.L.; Widyaningsih, P., Volterra integral equations solved in Fredholm form using Walsh functions, Anziam J., 45, E, C269-C282, (2004) · Zbl 1063.65590
[3] Chen, C.F.; Hsiao, C.H., Haar wavelet method for solving lumped and distributed parameter systems, IEEE proc.—control theory appl., 144, 1, 87-94, (1997) · Zbl 0880.93014
[4] Hsiao, C.H.; Wang, W.J., Optimal control of linear time-varying systems via Haar wavelets, J. optim. theory appl., 103, 3, 641-655, (1999) · Zbl 0941.49018
[5] R.T. Lynch, J.J. Reis, Haar transform image coding, in: Proceedings of the Conference on National Telecommunication, Dallas, TX, 1976, pp. 44.3-1-44.3.
[6] Razzaghi, M.; Nazarzadeh, J., Walsh functions, Wiley encyclopedia electr. electr. eng., 23, 429-440, (1999)
[7] J.J. Reis, R.T. Lynch, J. Butman, Adaptive Haar transform video bandwith reduction stem for RPV’s, in: Proceedings of the Annual Meeting on Society of Photo Optic Instrumentation Engineering (SPIE), San Diego, CA, 1976, pp. 24-35.
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