Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators
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- Auzinger W., Hofstätter H., Koch O. (2016) Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators. In: Gerdt V., Koepf W., Seiler W., Vorozhtsov E. (eds) Computer Algebra in Scientific Computing. CASC 2016. Lecture Notes in Computer Science, vol 9890. Springer, Cham
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.