Convergence of operator splittings for locally Lipschitz-continuous operators in Banach spaces

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Abstract

Operator splitting is analyzed in the general framework of Banach spaces. The convergence of sequential splitting and additive splitting is proven for problems with locally Lipschitz-continuous operators. Suitable time step size is calculated from the size of the set where the Lipschitz-property holds. Numerical examples are presented to confirm the theoretical results.

Keywords

Nonlinear ODE-s
Nonlinear PDE-s
Operator splitting
Convergence

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