Recently, Lodhi and Mishra (J Comput Appl Math 319:170–187, 2017) presented the standard B-spline method based on quintic B-spline basis functions to solve a type of singularly perturbed boundary value problems (SPBVP). We note that their method provides only fourth-order convergence approximation to the solution of such problem. In this paper, we present a novel optimal B-spline technique, based on same quintic B-spline basis function as used in Lodhi and Mishra (2017), for solving linear and nonlinear SPBVP. The advantage of the suggested method over the method in Lodhi and Mishra (2017) is that our method has sixth-order rate of convergence. To obtain higher order of convergence, a high-order perturbation of the SPBVP is generated. The method is tested for its efficiency by applying it on five test problems.

最近，Lodhi和Mishra（J Comput Appl Math 319：170–187，2017）提出了基于五次B样条基函数的标准B样条方法，以解决一类奇摄动边值问题（SPBVP）。我们注意到，他们的方法仅提供四阶收敛近似来解决此类问题。在本文中，我们基于Lodhi和Mishra（2017）中使用的相同五次B样条基函数，提出了一种新颖的最优B样条技术，用于求解线性和非线性SPBVP。与Lodhi和Mishra（2017）中的方法相比，建议的方法的优势在于我们的方法具有六阶收敛速度。为了获得更高的收敛阶，生成了SPBVP的高阶扰动。通过将其应用于五个测试问题来测试该方法的效率。