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Numerical solutions of ordinary differential equations with quadratic trigonometric splines. (English) Zbl 1068.65094
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.

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
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