bseries.jl

Trees, Algebras, and Differential Equations: Extending the B-series.jl package for numerical analysis of initial value problems

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Thu, Oct 10 2024

bseries.jl software numerical methods PDE

In this project we seek to extend the capabilities of bseries.jl to new classes of methods and/or new kinds of analysis. There are a number of possible directions and the specific one chosen will depend on the interests and knowledge of the student. Possibilities include extensions to:- Multi-derivative methods - Partitioned methods (e.g. for Hamiltonian systems) - General linear (multistep, multistage) methods - Exponential methods - Alternative bases for order conditions - Application of simplifying assumptions in method design - Generalized additive Runge-Kutta methods - Characterization of energy-preserving B-series - Extensions of B-series, such as aromatic B-series, exotic B-series, and S-series.