Modified collocation methods for second kind of volterra integral equations with weakly singular highly oscillatory bessel kernels

In this paper, we investigate the second kind of Volterra integral equations with weakly sinular highly oscillatory Bessel kernels by using two collocation methods: direct high-order interpolationorder (DO) and direct Hermite interpolation (DH). Based on hypergeometric and Gamma functions, we obtain a method for solving the modified moments f01 x alpha(1 - x)sJv(omega x)dx. Compared with the Filon-type (QFN) method, piecewise constant collocation N ) method and linear collocation (Q4/1 of the method through error analysis and numerical examples.