Asymptotic Expansions of the Cubic Spline Collocation Solution for Second-Order Ordinary Differential Equations

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In this paper, we consider the following problem $$\begin{cases}u''(x)=f(x,u(x),u'(x)), a\leq x\leq b,\\u(a)=u(b)=0,\end{cases}$$ and obtain the theorem.

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Asymptotic Expansions of the Cubic Spline Collocation Solution for Second-Order Ordinary Differential Equations. (1988). Journal of Computational Mathematics, 6(2), 156-163. https://gsp.tricubic.dev/JCM/article/view/10909