Operator splittings and spatial approximations for evolution equations
arXiv:0810.169424 citationsh-index: 14
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Provides theoretical convergence guarantees for operator splitting with spatial discretization, relevant for numerical analysis of evolution equations.
The paper investigates the convergence of operator splitting methods (sequential, Strang, weighted) when combined with spatial approximations, proving a variant of Chernoff's product formula and applying it to abstract partial delay differential equations.
The convergence of various operator splitting procedures, such as the sequential, the Strang and the weighted splitting, is investigated in the presence of a spatial approximation. To this end a variant of Chernoff's product formula is proved. The methods are applied to abstract partial delay differential equations.