ERROR ANALYSIS OF TRIGONOMETRIC INTEGRATORS FOR SEMILINEAR WAVE EQUATIONS

作者：Gauckler Ludwig^*

来源：SIAM Journal on Numerical Analysis, 2015, 53(2): 1082-1106.

DOI：10.1137/140977217

• nonlinear wave equation
• semilinear wave equation
• trigonometric integrators
• exponential integrators
• Stormer-Verlet method
• leapfrog method
• error bounds

An error analysis of trigonometric integrators (or exponential integrators) applied to spatial semidiscretizations of semilinear wave equations with periodic boundary conditions in one space dimension is given. In particular, optimal second-order convergence is shown requiring only that the exact solution is of finite energy. The analysis is uniform in the spatial discretization parameter. It covers the impulse method which coincides with the method of Deuflhard and the mollified impulse method of Garcia-Archilla, Sanz-Serna, and Skeel as well as the trigonometric methods proposed by Hairer and Lubich and by Grimm and Hochbruck. The analysis can also be used to explain the convergence behavior of the Stormer-Verlet/leapfrog time discretization.

• 出版日期2015