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This paper studies a class of convolution quadratures, well-known numericalmethods for calculation of convolution integrals. In contrast to the existingcounterpart, which uses the linear multistep formula or Runge-Kutta method, weemploy the block generalized Adams method to discretize the underlying initialvalue problem. Similar to the convolution quadrature method based on the linearmultistep formula, the proposed method can also be implemented on an equispacedgrid. In addition, the proposed approach is as stable as the convolutionquadrature based on the Runge-Kutta method, which indicates that it canaccurately solve a wide range of problems without becoming unstable. We providea detailed convergence analysis for the proposed convolution quadrature methodand numerically illustrate our theoretical findings for convolution integralswith smooth and weakly singular kernels.

Convolution quadratures based on block generalized Adams methods