Document Type: Research Paper
Department of Science, School of Mathematical Sciences, University of Zabol, Zabol, Iran
Faculty of Engineering, Sabzevar University of New Technology, Sabzevar, Iran
We present a method for calculating the numerical approximation of the two-dimensional mixed Volterra Fredholm integral equations, using the properties of the rationalized Haar (RH) wavelets and the matrix operator. Attaining this purpose, first, an operator and then an orthogonal projection should be defined. Regarding the characteristics of Haar wavelet, we solve the integral equation without using common mathematical methods. An upper bound and the convergence of the mentioned method have been proved, by using the Banach fixed point. Moreover, the rate of the convergence method is $O(n(2q) ^n)$. Finally, several examples of different kinds of functions are presented and solved by this method.