Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators
We describe a package realized in the Julia programming language which performs symbolic manipulations applied to nonlinear evolution equations, their flows, and commutators of such objects. This tool was employed to perform contrived computations arising in the analysis of the local error of operator splitting methods. It enabled the proof of the convergence of the basic method and of the asymptotical correctness of a defect-based error estimator. The performance of our package is illustrated on several examples.
KeywordsNonlinear evolution equations Time integration Splitting methods Symbolic computation Julia language
This work was supported in part by the projects P24157-N13 of the Austrian Science Fund (FWF) and MA14-002 of the Vienna Science and Technology Fund (WWTF).
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