In this paper, we develop a class of methods based on exponential spline at off-step points for the solution of the nonlinear and linear fourth-order boundary value problems (BVPs). Spline relations and boundary equations are developed, and the methods of order two, four and six have been obtained. Convergence analysis of the method is discussed. Numerical examples for linear and nonlinear BVPs are given to illustrate the efficiency of our method, and results are compared with other known methods.

中文翻译：

---

板挠度理论中边值问题的指数样条解

在本文中，我们开发了一种基于指数样条的离阶点方法，用于解决非线性和线性四阶边值问题（BVP）。建立了样条关系和边界方程，并获得了二阶，四阶和六阶方法。讨论了该方法的收敛性分析。给出了线性和非线性BVP的数值示例，以说明我们的方法的效率，并将结果与​​其他已知方法进行了比较。