MODIFIED COLLOCATION METHODS FOR SECOND KIND OF VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR HIGHLY OSCILLATORY BESSEL KERNELS

Abstract

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 $ \int_{0}^{1}x^{\alpha}(1-x)^{\beta}J_{v}(\omega x)dx $. Compared with the Filon-type $ (Q_{N}^{F}) $ method, piecewise constant collocation $ (Q_{N}^{L, 0}) $ method and linear collocation $ (Q_{N}^{L, 1}) $ method, we verified the efficiency of the method through error analysis and numerical examples.