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| In this talk, the approach of operator splitting for the efficient time integration of different classes of partial differential equations is discussed. In particular, a compact local error representation for the first-order Lie-Trotter splitting method is deduced and applied to the Westervelt equation, a nonlinear damped wave equation that arises in nonlinear acoustics as mathematical model for the propagation of sound waves in high intensity ultrasound applications. The resulting global error estimate confirms that the Lie-Trotter splitting method remains stable and that the nonstiff convergence order is retained in situations where the problem data are sufficiently regular. Numerical examples illustrate and complement the theoretical investigations. |
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