A Julia package for generating order conditions for splitting methods.
For more information, see the examples below and the papers:
W. Auzinger, H. Hofstätter, D. Ketcheson, O. Koch, Practical Splitting Methods for the Adaptive Integration of Nonlinear Evolution Equations. Part I: Construction of Optimized Schemes and Pairs of Schemes, BIT Numer. Math. (2016), doi:10.1007/s10543-016-0626-9.
The newest version contains a Julia interface to FORM, a Symbolic Manipulation System which is used to generate optimized Julia functions from the multivariate polynomial equations representing order conditions for splitting methods. These optimized Julia functions then serve as input for some Julia Nonlinear Optimization package.
generate_equations(q,s) of this package implements the following algorithm:
##Installation In a Julia notebook type
##Examples To get easy access to the examples, copy them into the home directory:
cp(joinpath(homedir(), ".julia/v0.4/SplittingOrderConditions/examples/"), joinpath(homedir(), "SplittingOrderConditions_examples"), remove_destination=true)
Then 'SplittingOrderConditions_examples' will be listed in the JuliaBox home screen. The examples contain among others