Modified asymptotic orders of the direct Filon method for a class of Volterra integral equations

The direct Filon method provides efficient approximation for solutions of Volterra integral equations with highly oscillatory kernels. In this paper, we study the rate of convergence of this method for a class of equations with trigonometric kernels. The asymptotic order is developed by examining the property of the solution. Numerical experiments are included to verify the given order.