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Vietnam Journal of Mathematics 39:2 (2011) 145-157

Improving the Solution of Nonlinear Volterra Integral Equations

Using Rationalized Haar s-Functions

S.M. Hashemiparast1, M. Sabzevari1,2 and H. Fallahgoul1

1Department of Mathematics, Faculty of science, K.N. Toosi University of

Technology, P.O. Box 16315−1618, Tehran, Iran

2Department 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 s-functions 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 coecients, 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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