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Vietnam
Journal of Mathematics 39:2 (2011) 145157

Improving the Solution of Nonlinear Volterra
Integral Equations
Using Rationalized Haar sFunctions

S.M. Hashemiparast^{1}, M.
Sabzevari^{1,2} and H. Fallahgoul^{1}

^{1}Department
of Mathematics, Faculty of science, K.N. Toosi
University of
Technology, P.O. Box 16315−1618, Tehran,
Iran
^{2}Department
of Mathematics, Faculty of science, University of Kashan,
Kashan, Iran
^{ }

Abstract. In this paper, we propose a new modiﬁcation
of rationalized Haar functions called rationalized Haar sfunctions for the
numerical solution of linear and nonlinear Volterra integral equations of
the second kind. By selecting these functions and following the procedure
of determining the wavelet expansion coeﬃcients, the calculations are economized. This method converts the
integral equation to a system of equations containing an identity matrix
which simpliﬁes the calculations. Finally by using numerical
examples the accuracy of the solution is illustrated.

2000 Mathematics
Subject Classification. 65T60, 45B05, 45D05.

Keywords.
Rationalized Haar functions; Volterra integral equations of the second
kind; System of linear and nonlinear equations; Operational matrix.

Email: sabzevari@dena.kntu.ac.ir
[Corresponding Author]


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