Grimm, Volker; Hochbruck, Marlis Error analysis of exponential integrators for oscillatory second-order differential equations. (English) Zbl 1093.65078 J. Phys. A, Math. Gen. 39, No. 19, 5495-5507 (2006). Authors’ abstract: We analyse a family of exponential integrators for second-order differential equations in which high frequency oscillations in the solution are generated by a linear part. Conditions are given which guarantee that the integrators allow second-order error bounds independent of the product of the step size with the frequencies. Our convergence analysis generalizes known results on the modified impulse method by B. García Archilla, J. M. Sanz-Serna and R. D. Skeel [SIAM. J. Sci. Comput. 20, 930–963 (1999; Zbl 0927.65143) and on Gautschi-type exponential integrators [E. Hairer, C. Lubich and G. Wanner, Geometric numerical integration. (Berlin: Springer) (2002; Zbl 0994.65135); M. Hochbruck and C. Lubich, Numer. Math. 83, 403-426 (1999; Zbl 0937.65077)]. Reviewer: Fuhua Ling (Milpitas) Cited in 45 Documents MSC: 65L70 Error bounds for numerical methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 31C10 Pluriharmonic and plurisubharmonic functions Keywords:Exponential integrator; oscillatory second-order differential equation; convergence analysis; error bounds Citations:Zbl 0927.65143; Zbl 0994.65135; Zbl 0937.65077 PDFBibTeX XMLCite \textit{V. Grimm} and \textit{M. Hochbruck}, J. Phys. A, Math. Gen. 39, No. 19, 5495--5507 (2006; Zbl 1093.65078) Full Text: DOI