In this study, an effective and rapidly convergent analytical technique is introduced to obtain approximate analytical solutions for nonlinear differential equations. The technique is a combination of the optimal quasilinearization method and the Picard iteration method. The optimal quasilinearization method is used to reduce the nonlinear differential equation to a sequence of linearized differential equations and the Picard iteration method is applied to get the approximate solutions of the linearized equations arising from the optimal quasilinearization method. The convergence analysis of the technique is also discussed. To determine the efficiency and effectiveness of the technique, we consider two numerical examples from real-world applications. The proposed method can easily be extended to a wide class of nonlinear differential equations also.

在这项研究中，引入了一种有效且快速收敛的分析技术来获得非线性微分方程的近似解析解。该技术是最优拟线性化方法和皮卡德迭代方法的结合。采用最优拟线性化方法将非线性微分方程化简为线性化微分方程序列，并应用Picard迭代法得到最优拟线性化方法得到的线性化方程的近似解。还讨论了该技术的收敛性分析。为了确定该技术的效率和有效性，我们考虑了来自实际应用的两个数值示例。