In this paper, we mainly study an exponential spline function space, construct a basis with local supports, and present the relationship between the function value and the first and the second derivative at the nodes. Using these relations, we construct an exponential spline-based difference scheme for solving a class of boundary value problems of second-order ordinary differential equations (ODEs) and analyze the error and the convergence of this method. The results show that the algorithm is high accurate and conditionally convergent, and an accuracy of was achieved with smooth functions.

中文翻译：

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一类二阶常微分方程边值问题的指数样条差分格式

在本文中，我们主要研究指数样条函数空间，构造具有局部支持的基础，并给出节点处函数值与一阶和二阶导数之间的关系。利用这些关系，我们构造了一种基于指数样条的差分格式，用于求解一类二阶常微分方程（ODE）的边值问题，并分析了该方法的误差和收敛性。结果表明，该算法具有较高的精确度和条件收敛性，且精度为 通过平滑的功能实现。