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.

翻译：本文研究了一类卷积求积法——一种用于高效计算卷积积分的数值技术。我们采用块广义Adams方法对基础初值问题进行离散化处理，区别于依赖线性多步公式或Runge-Kutta方法的传统方案。所提出的卷积求积法可在无需调整网格点的前提下动态控制收敛阶数，从而提升计算灵活性。通过局部插值多项式与块尺寸的策略性选择，该方法在计算双曲型核函数的卷积积分时能实现高阶收敛。我们对所提出的卷积求积法进行了严格的收敛性分析，并针对多种卷积积分进行了数值验证以支撑理论结论。