This paper deals with the construction of a functionally fitted method for solving first-order differential systems whose solutions present an oscillatory behaviour. The method incorporates the second derivative to obtain better accuracies and is developed on the basis that it provides no errors when the true solution is a linear combination of some trigonometric and exponential functions containing a parameter. The main properties of the method are presented, showing a fourth-order convergence. Some numerical experiments are included to show the good performance of the proposed method.

中文翻译：

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振荡初值问题最大阶次的二阶导数函数拟合方法

本文讨论了一种用于求解一阶微分系统的函数拟合方法的构造，该系统的解呈现振荡行为。该方法结合了二阶导数以获得更好的精度，并且在真实解是一些包含参数的三角函数和指数函数的线性组合时它不会提供错误的基础上开发。介绍了该方法的主要特性，显示了四阶收敛性。包括一些数值实验以表明所提出方法的良好性能。