Error analysis of one-stage explicit extended RKN integrators for semilinear wave equations

Bin Wang; Xinyuan Wu

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Error analysis of one-stage explicit extended RKN integrators for semilinear wave equations

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arxiv 1801.02070 v1 pith:XD3BRWUS submitted 2018-01-06 math.NA cs.NA

Error analysis of one-stage explicit extended RKN integrators for semilinear wave equations

Bin Wang , Xinyuan Wu This is my paper

classification math.NA cs.NA

keywords analysisequationserrorexplicitextendedintegratorsone-stagesemilinear

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In this paper, we present an error analysis of one-stage explicit extended Runge--Kutta--Nystr\"{o}m integrators for semilinear wave equations. These equations are analysed by using spatial semidiscretizations with periodic boundary conditions in one space dimension. Optimal second-order convergence is proved without requiring Lipschitz continuous and higher regularity of the exact solution. Moreover, the error analysis is not restricted to the spectral semidiscretization in space.

Error analysis of one-stage explicit extended RKN integrators for semilinear wave equations

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