Papers › Runge--Kutta generalized Convolution Quadrature for sectorial problems
Runge--Kutta generalized Convolution Quadrature for sectorial problems
Jing Guo, Maria Lopez-Fernandez
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We study the application of the generalized convolution quadrature (gCQ) based on Runge--Kutta methods to approximate the solution of an important class of sectorial problems. The gCQ generalizes Lubich's original convolution quadrature (CQ) to variable steps. High-order versions of the gCQ have been developed in the last decade, relying on certain Runge--Kutta methods. The Runge--Kutta based gCQ has been studied so far in a rather general setting, which includes applications to boundary integral formulations of wave problems. The available stability and convergence results for these new methods are suboptimal compared to those known for the uniform-step CQ, both in terms of convergence order and regularity requirements of the data. Here we focus on a special class of sectorial problems and prove that in these important applications it is possible to achieve the same order of convergence as for the original CQ, under the same regularity hypotheses on the data, and for very general time meshes. In the particular case of data with some known algebraic type of singularity, we also show how to choose an optimally graded time mesh to achieve convergence with maximal order, overcoming the well-known order reduction of the original CQ in these situations. An important advantage of the gCQ method is that it allows for a fast and memory-efficient implementation. We describe how the fast and oblivious Runge--Kutta based gCQ can be implemented and illustrate our theoretical results with several numerical experiments. The codes implementing the examples in this article are available in [13].
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections