In this paper, we apply an accelerated version of the Adomian decomposition method for solving a class of nonlinear partial differential equations. This version is a smart recursive technique in which no differentiation for computing the Adomian polynomials is needed. Convergence analysis of this version is discussed, and the error of the series solution is estimated. Some numerical examples were solved, and the numerical results illustrate the effectiveness of this version.

中文翻译：

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一类非线性偏微分方程的加速解

在本文中，我们使用Adomian分解方法的加速版本来求解一类非线性偏微分方程。此版本是一种智能递归技术，无需为计算Adomian多项式而进行微分。讨论了该版本的收敛性分析，并估计了级数解的误差。解决了一些数值示例，数值结果说明了该版本的有效性。