Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
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AbstractWe present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.
CitationPractical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes 2016 BIT Numerical Mathematics
SponsorsOpen access funding provided by Technische Universität Wien. This work was supported by the Austrian Science Fund (FWF) under Grant P24157-N13, and by the Vienna Science and Technology Fund (WWTF) under Grant MA-14-002. The computational results presented have been achieved in part using the Vienna Scientific Cluster (VSC).
JournalBIT Numerical Mathematics