TL;DR
This paper introduces BSeries.jl, a Julia package that enables efficient computation and manipulation of B-series, facilitating advanced analysis and design of differential equation discretizations.
Contribution
The paper presents a high-performance Julia package for B-series, including theoretical background, practical examples, and capabilities for high-order computations.
Findings
Efficient computation of high-order B-series.
Applications demonstrated in method composition.
Supports backward error analysis.
Abstract
We present BSeries.jl, a Julia package for the computation and manipulation of B-series, which are a versatile theoretical tool for understanding and designing discretizations of differential equations. We give a short introduction to the theory of B-series and associated concepts and provide examples of their use, including method composition and backward error analysis. The associated software is highly performant and makes it possible to work with B-series of high order.
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