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arXiv · 2305.11134

Generalized convolution quadrature based on the trapezoidal rule

Lehel Banjai·Matteo Ferrari
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Abstract

We present a novel generalized convolution quadrature method that accurately approximates convolution integrals. During the late 1980s, Lubich introduced convolution quadrature techniques, which have now emerged as a prevalent methodology in this field. However, these techniques were limited to constant time stepping, and only in the last decade generalized convolution quadrature based on the implicit Euler and Runge-Kutta methods have been developed, allowing for variable time stepping. In this paper, we introduce and analyze a new generalized convolution quadrature method based on the trapezoidal rule. Crucial for the analysis is the connection to a new modified divided difference formula that we establish. Numerical experiments demonstrate the effectiveness of our method in achieving highly accurate and reliable results.

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Lehel Banjai, Matteo Ferrari. 2023-05-18. Generalized convolution quadrature based on the trapezoidal rule. https://arxiv.org/abs/2305.11134

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