Convolution quadrature and discretized operational calculus I.
Numerische Mathematik
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Some new problems in numerical integration
Journal of Computational and Applied Mathematics
Rapid Solution of the Wave Equation in Unbounded Domains
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
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In the last years several authors have used Lubich convolution quadrature formulas to discretize space-time boundary integral equations representing time dependent problems. These rules have the fundamental property of not using explicitly the expression of the kernel of the integral equation they are applied to, which is instead replaced by that of its Laplace transform, usually given by a simple analytic function. In this paper, a review of these rules, which includes their main properties, several new remarks and some conjectures, will be presented when they are applied to the heat and wave space-time boundary integral equation formulations. The construction and behavior of the corresponding coefficients are analyzed and tested numerically. When the quadrature is defined by a BDF method, a new approach for the representation of its coefficients is presented.