Convolution quadratures based on block generalized Adams methods

Abstract

This paper studies a family of convolution quadratures, a numerical technique for efficient evaluation of convolution integrals. We employ the block generalized Adams method to discretize the underlying initial value problem, departing from the well-established approaches that rely on linear multistep formulas or Runge-Kutta methods. The convergence order of the proposed convolution quadrature can be dynamically controlled without requiring grid point adjustments, enhancing exibility. Through strategic selection of the local interpolation polynomial and block size, the method achieves high-order convergence for calculation of convolution integrals with hyperbolic kernels. We provide a rigorous convergence analysis for the proposed convolution quadrature and numerically validate our theoretical findings for various convolution integrals.