Operator splitting for dissipative delay equations
arXiv:1009.198111 citationsh-index: 14
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Provides a theoretical foundation for operator splitting methods in a class of delay differential equations, which is incremental for numerical analysis.
The authors prove convergence and analyze the order of convergence for Lie-Trotter splitting applied to nonlinear delay equations with dissipation, supported by numerical examples.
We investigate Lie-Trotter product formulae for abstract nonlinear evolution equations with delay. Using results from the theory of nonlinear contraction semigroups in Hilbert spaces, we explain the convergence of the splitting procedure. The order of convergence is also investigated in detail, and some numerical illustrations are presented.