This paper presents a numerical algorithm for solving high-order BVPs. We introduce the construction method of multiscale orthonormal basis in $W^{m}_{2}[0,1]$ . Based on the orthonormal basis, the numerical solution of the boundary value problem is obtained by finding the ε-approximate solution. In addition, the convergence order, stability, and time complexity of the method are discussed theoretically. At last, several numerical experiments show the feasibility of the proposed method.

中文翻译：

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高阶边值问题的一种新方法

本文提出了一种求解高阶BVP的数值算法。我们介绍了$ W ^ {m} _ {2} [0,1] $中的多尺度正交基的构造方法。在正交基础上，通过找到ε近似解来获得边值问题的数值解。另外，从理论上讨论了该方法的收敛顺序，稳定性和时间复杂度。最后，通过数值实验证明了该方法的可行性。