On superconvergence of Runge–Kutta convolution quadrature for the wave equation

نویسندگان

چکیده

Abstract The semidiscretization of a sound soft scattering problem modelled by the wave equation is analyzed. spatial treatment done integral methods. Two temporal discretizations based on Runge–Kutta convolution quadrature are compared: one relies incoming as input data and other its derivative. convergence rate latter shown to be higher than previously established in literature. Numerical results indicate sharpness analysis. proof hinges novel estimate Dirichlet-to-Impedance map for certain Helmholtz problems. Namely, frequency dependence can lowered power $$\left| s\right| $$ s (up logarithmic term polygonal domains) compared Dirichlet-to-Neumann map.

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ژورنال

عنوان ژورنال: Numerische Mathematik

سال: 2021

ISSN: ['0945-3245', '0029-599X']

DOI: https://doi.org/10.1007/s00211-020-01161-9