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Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions. (English) Zbl 1146.65082
Summary: We propose a simple efficient direct method for solving Volterra integral equation of the first kind. By using block-pulse functions and their operational matrix of integration, first kind integral equation can be reduced to a linear lower triangular system which can be directly solved by forward substitution. Some examples are presented to illustrate efficiency and accuracy of the proposed method.

65R20Integral equations (numerical methods)
45D05Volterra integral equations
Full Text: DOI
[1] Akyüz-Daşcioǧlu, A.: A Chebyshev polynomial approach for linear Fredholm-Volterra integro-differential equations in the most general form, Appl. math. Comput. 181, 103-112 (2006) · Zbl 1148.65318 · doi:10.1016/j.amc.2006.01.018
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[3] E. Babolian, A. Salimi Shamloo, Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions, J. Comput. Appl. Math., in press, doi: 10.1016/j.cam.2007.03.007. · Zbl 1135.65043
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[7] Maleknejad, K.; Derili, H.: Numerical solution of integral equations by using combination of spline-collocation method and Lagrange interpolation, Appl. math. Comput. 175, 1235-1244 (2006) · Zbl 1093.65125 · doi:10.1016/j.amc.2005.08.034
[8] Rashed, M. T.: An expansion method to treat integral equations, Appl. math. Comput. 135, 65-72 (2003) · Zbl 1023.65135 · doi:10.1016/S0096-3003(01)00311-3
[9] Tikhonov, A. N.; Arsenin, V. Y.: Solutions of ill-posed problems, (1977) · Zbl 0354.65028