Two-point boundary value problems are commonly used as a numerical test in developing an efficient numerical method. Several researchers studied the application of a cubic non-polynomial spline method to solve the two-point boundary value problems. A preliminary study found that a cubic non-polynomial spline method is better than a standard finite difference method in terms of the accuracy of the solution. Therefore, this paper aims to examine the performance of a cubic non-polynomial spline method through the combination with the full-, half-, and quarter-sweep iterations. The performance was evaluated in terms of the number of iterations, the execution time and the maximum absolute error by varying the iterations from full-, half- to quarter-sweep. A successive over-relaxation iterative method was implemented to solve the large and sparse linear system. The numerical result showed that the newly derived QSSOR method, based on a cubic non-polynomial spline, performed better than the tested FSSOR and HSSOR methods.

两点边值问题通常用作开发有效数值方法的数值测试。一些研究人员研究了三次非多项式样条方法在解决两点边值问题中的应用。初步研究发现三次非多项式样条法在求解精度方面优于标准有限差分法。因此，本文旨在通过结合全扫描、半扫描和四分之一扫描迭代来检验三次非多项式样条方法的性能。通过改变从全扫描、半扫描到四分之一扫描的迭代，根据迭代次数、执行时间和最大绝对误差来评估性能。采用逐次超松弛迭代法求解大而稀疏的线性系统。数值结果表明，新推导出的基于三次非多项式样条的 QSSOR 方法的性能优于测试的 FSSOR 和 HSSOR 方法。