Volume 10, Issue 2
Spline Collocation Approximation to Periodic Solutions of Ordinary Differential Equations

Li-qing Zhang

DOI:

J. Comp. Math., 10 (1992), pp. 147-154

Published online: 1992-10

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  • Abstract

A spline collocation method is proposed to approximate the periodic solution of nonlinear ordinary differential equations. It is proved that the cubic periodic spline collocation solution has the same error bound $O(h^4)$ and superconvergence of the derivative at collocation points as that of the interpolating spline function. Finally a numerical example is given to demonstrate the effectiveness of our algorithm.

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@Article{JCM-10-147, author = {}, title = {Spline Collocation Approximation to Periodic Solutions of Ordinary Differential Equations}, journal = {Journal of Computational Mathematics}, year = {1992}, volume = {10}, number = {2}, pages = {147--154}, abstract = { A spline collocation method is proposed to approximate the periodic solution of nonlinear ordinary differential equations. It is proved that the cubic periodic spline collocation solution has the same error bound $O(h^4)$ and superconvergence of the derivative at collocation points as that of the interpolating spline function. Finally a numerical example is given to demonstrate the effectiveness of our algorithm. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9347.html} }
TY - JOUR T1 - Spline Collocation Approximation to Periodic Solutions of Ordinary Differential Equations JO - Journal of Computational Mathematics VL - 2 SP - 147 EP - 154 PY - 1992 DA - 1992/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9347.html KW - AB - A spline collocation method is proposed to approximate the periodic solution of nonlinear ordinary differential equations. It is proved that the cubic periodic spline collocation solution has the same error bound $O(h^4)$ and superconvergence of the derivative at collocation points as that of the interpolating spline function. Finally a numerical example is given to demonstrate the effectiveness of our algorithm.
Li-qing Zhang. (1970). Spline Collocation Approximation to Periodic Solutions of Ordinary Differential Equations. Journal of Computational Mathematics. 10 (2). 147-154. doi:
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