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bseries.jl
Trees, Algebras, and Differential Equations: Extending the B-series.jl package for numerical analysis of initial value problems
Apply to this project
Thu, Oct 10 2024
Internship
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.
