In this paper, we construct a four‐stage explicit improved Runge–Kutta direct (IRKD) method of order six for solving special third‐order ordinary differential equations. The sixth‐order IRKD method is a two‐step method and it requires fewer number of stages compared to the classical Runge–Kutta method of the same order per step. The stability properties of the proposed method are given. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method compared with the existing methods in the literature.

中文翻译：

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特殊三阶常微分方程的六阶改进Runge-Kutta直接方法

在本文中，我们构造了四阶显式改进的六阶Runge-Kutta直接（IRKD）方法，用于求解特殊的三阶常微分方程。六阶IRKD方法是一种两步方法，与每步相同阶数的经典Runge-Kutta方法相比，它需要的级数更少。给出了所提方法的稳定性。数值结果表明，与文献中的现有方法相比，该方法的有效性和准确性。