In this paper, a nonpolynomial spline technique is used for developing a new algorithm for solving systems of second-order boundary value problems. Convergence analysis of the algorithm has been carried out which shows that the algorithm is second- as well as fourth-order convergent. In addition to that, four numerical problems including linear, nonlinear and singularly perturbed systems are given to prove the effectiveness and applicability of the developed algorithm. The numerical results show that the developed algorithm is better than the existing methods for solving systems of second-order boundary value problems.

中文翻译：

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用非多项式样条技术求解广义二阶边值问题的新算法

本文采用非多项式样条技术开发了一种新的算法来求解二阶边值问题。对该算法进行了收敛分析，结果表明该算法是二阶和四阶收敛的。除此之外，还给出了包括线性，非线性和奇摄动系统在内的四个数值问题，以证明该算法的有效性和适用性。数值结果表明，该算法优于现有的求解二阶边值问题的方法。