Numerical solution of volterra integral equations with weakly singular kernel using legendre wavelet method

The presented paper investigates a new numerical method based on the characteristics of Legendre wavelet for solving Volterra Integral equations in this method,With the help of block-pulse functions and their characteristics, we obtain the fractional integral operational matrices corresponding to these wavelets. Then, by introducing collocation points, we use them to convert the desired equations into a system of algebraic equations. After solving the device, the approximate solution of the equation is easily calculated. Finally, we provide some numerical examples to demonstrate the accuracy and efficiency of the proposed methods.