In this paper we like to explore the full power of Adomian decomposition method (ADM), specially its symbolic capability. We will demonstrate the standard ADM and ADM with integration factor to compute explicit closed form solutions of first order scalar partial differential equations with unprescribed initial conditions, and even with parameters. These features are those numerical methods fail to do. Our examples include linear/nonlinear, constant/variable coefficients and homogeneous/nonhomogeneous equations. The method of characteristics is also tested and compared with these two ADM methods. We conclude that ADM is excellent among all existing methods.

在本文中，我们希望探索Adomian分解方法（ADM）的全部功能，尤其是其符号功能。我们将演示标准ADM和具有积分因子的ADM，以计算具有未指定初始条件甚至参数的一阶标量偏微分方程的显式闭合形式解。这些功能是那些数值方法无法做到的。我们的示例包括线性/非线性，常数/可变系数和齐次/非齐次方程。还测试了特性方法，并与这两种ADM方法进行了比较。我们得出结论，在所有现有方法中，ADM都是出色的。