Nikolis, Athanassios Numerical solutions of ordinary differential equations with quadratic trigonometric splines. (English) Zbl 1068.65094 Appl. Math. E-Notes 4, 142-149 (2004). Summary: We present a numerical method for solving ordinary differential equations with quadratic trigonometric splines. This is a modification of a method, due to F.R. Loscalzo and T. D. Talbot [SIAM J. Numer. Anal. 4, 433–445 (1967; Zbl 0171.36301)], in which the approximations were made using only polynomial splines. If the solution is trigonometric or periodical, then trigonometric splines in general give better results. In the following analysis we are going to prove that the convergence of this numerical method is quadratic. This theoretical result agrees with numerical experiments. Cited in 10 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems Keywords:initial value problems; quadratic trigonometric splines; convergence; numerical experiments Citations:Zbl 0171.36301 PDFBibTeX XMLCite \textit{A. Nikolis}, Appl. Math. E-Notes 4, 142--149 (2004; Zbl 1068.65094) Full Text: EuDML EMIS