Generalized quadrature method for Volterra integral equation with highly oscillatory Bessel-trigonometric kernels
摘要
Volterra integral equations with highly oscillatory structures are difficult to solve directly. This paper introduces the generalized quadrature rule and constructs a two-point generalized quadrature method for Volterra integral equations of the second kind, which contains highly oscillatory Bessel-trigonometric kernels. The convergence analysis indicates that the proposed method achieves precise approximation effects under high-frequency oscillations and a large number of nodes. Numerical examples are provided to demonstrate the effectiveness of the generalized quadrature method in addressing highly oscillatory Volterra integral equations with Bessel-trigonometric kernels. The results indicate that both the oscillation frequency and the number of mesh nodes increase accuracy.