Abstract The main aim of this article is to use a new and simple algorithm namely the modified variational iteration algorithm-II (MVIA-II) to obtain numerical solutions of different types of fifth-order Korteweg-de Vries (KdV) equations. In order to assess the precision, stability and accuracy of the solutions, five test problems are offered for different types of fifth-order KdV equations. Numerical results are compared with the Adomian decomposition method, Laplace decomposition method, modified Adomian decomposition method and the homotopy perturbation transform method, which reveals that the MVIA-II exceptionally productive, computationally attractive and has more accuracy than the others.

中文翻译：

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五阶KdV方程数值解的一种有效方法

摘要 本文的主要目的是使用一种新的简单算法，即修正变分迭代算法-II (MVIA-II) 来获得不同类型的五阶 Korteweg-de Vries (KdV) 方程的数值解。为了评估解的精度、稳定性和准确性，针对不同类型的五阶 KdV 方程提供了五个测试问题。数值结果与Adomian分解法、拉普拉斯分解法、修正Adomian分解法和同伦微扰变换法进行了比较，表明MVIA-II异常高效，计算上有吸引力并且比其他方法具有更高的准确性。