Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators
Provides a computational tool for researchers analyzing operator splitting methods for nonlinear evolution equations.
The authors developed a Julia package for symbolic manipulation of flows of nonlinear evolution equations, enabling the proof of convergence of split-step time integrators and the correctness of a defect-based error estimator.
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.