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Modification of block pulse functions and their application to solve numerically Volterra integral equation of the first kind. (English) Zbl 1221.65338

Summary: A modification of block pulse functions is introduced and used to solve Volterra integral equation of the first kind. Some theorems are included to show convergence and advantage of the method. Some examples show accuracy of the method.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
Full Text: DOI

References:

[1] K.G. Steffens, The History of Approximation Theory: From Euler to Brenstein, Birkhauser pub., Boston 2006 ISBN 0817643532.; K.G. Steffens, The History of Approximation Theory: From Euler to Brenstein, Birkhauser pub., Boston 2006 ISBN 0817643532.
[2] Jiang, Z. H.; Schaufelberger, W., Block Pulse Functions and Their Applications in Control Systems (1992), Springer-Verlag pub: Springer-Verlag pub Berlin · Zbl 0771.93016
[3] Maleknejad, K.; Tavassoli-Kajani, M., Solving linear integro-differential equation system by Galerkin methods with hybrid functions, Appl Math Comput, 159, 603-612 (2004) · Zbl 1063.65145
[4] Maleknejad, K.; Mahmoudi, Y., Numerical solution of linear Fredholm integral equations by using hybrid Taylor and Block Pulse functions, Appl Math Comput, 149, 799-806 (2004) · Zbl 1038.65147
[5] Maleknejad, K.; Tavassoli-Kajani, M., Second kind integral equations by Galerkin methods with hybrid Legandre and Block Pulse functions, Appl Math Comput, 145, 623-629 (2003) · Zbl 1101.65323
[6] Maleknejad, K.; Sohrabi, S.; Baranji, B., Application of 2D-BPFs to nonlinear integral equations, Commun Nonlinear Sci Numer Simulat, 15, 527-535 (2010) · Zbl 1221.65339
[7] Babolian, E.; Masouri, Z., Direct method to solve Volterra integral equation of the first kind using operational matrix with Block Pulse Functions, Comput Appl Math, 220, 51-57 (2000) · Zbl 1146.65082
[8] Lepik, U., Haar wavelet method for nonlinear integro-differential equations, Appl Math Comput, 176, 324-333 (2006) · Zbl 1093.65123
[9] Rudin, W., Principles of Mathematical Analysis (1976), McGraw-Hill: McGraw-Hill Singapore · Zbl 0148.02903
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