A new numerical learning approach namely Rational Gegenbauer Least Squares Support Vector Machines (RG_LS_SVM), is introduced in this paper. RG_LS_SVM method is a combination of collocation method based on rational Gegenbauer functions and LS_SVM method. This method converts a nonlinear high order model on a semi-infinite domain to a set of linear/nonlinear equations with equality constraints which decreases computational costs. Blasius, Falkner–Skan and MHD Falkner–Skan models and the effects of various parameters over them are investigated to satisfy accuracy, validity and efficiency of the proposed method. Both Primal and Dual forms of the problems are considered and the nonlinear models are converted to linear models by applying quasilinearization method to get the better results. Comparing the results of RG_LS_SVM method with available analytical and numerical solutions show that the present methods are efficient and have fast convergence rate and high accuracy.

中文翻译：

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一种求解一般 Falkner-Skan 模型的新数值学习方法

本文介绍了一种新的数值学习方法，即 Rational Gegenbauer 最小二乘支持向量机 (RG_LS_SVM)。RG_LS_SVM 方法是基于有理 Gegenbauer 函数的搭配方法和 LS_SVM 方法的组合。该方法将半无限域上的非线性高阶模型转换为一组具有等式约束的线性/非线性方程，从而降低了计算成本。Blasius、Falkner-Skan 和 MHD Falkner-Skan 模型以及各种参数对它们的影响进行了研究，以满足所提出方法的准确性、有效性和效率。考虑了问题的原始形式和对偶形式，并通过应用拟线性化方法将非线性模型转换为线性模型以获得更好的结果。