In this paper, we describe an optimal B-spline collocation method to solve one-dimensional non-linear Bratu problem. Convergence result of the method is established through Green’s function technique and it is proved that the method has sixth order convergence. The applicability and accuracy of the method are demonstrated through two numerical examples. It is shown that the computational result is consistent with theoretical prediction. Moreover, the numerical results obtained by the present method are compared with those obtained by two other B-spline collocation approaches reported in the literature. The computed results reveal that our method is accurate and easy to implement.

中文翻译：

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求解Bratu问题的六阶最优B样条搭配方法

在本文中，我们描述了一种解决一维非线性 Bratu 问题的最优 B 样条搭配方法。通过格林函数技术建立了该方法的收敛性结果，证明了该方法具有六阶收敛性。通过两个数值算例证明了该方法的适用性和准确性。结果表明，计算结果与理论预测一致。此外，将本方法获得的数值结果与文献中报道的另外两种 B 样条搭配方法获得的数值结果进行了比较。计算结果表明我们的方法准确且易于实现。