双重分解法及其与Adomian分解法的比较

Comparison Between Adomian Double Decomposion Method and Adomian Decomposion Method

在求解初边值问题Adomian分解法的基础上,研究了求二维偏微分方程边值问题的双重Adomian分解法,对Adomian分解法的初始项作了进一步分解,使逆算符分解法得到了改进。通过具体微分方程算例对双重分解法和Adomian分解法进行了比较,验证了双重分解算法的有效性。这一改进的分解算法既能提高精度又能减少计算量,而且还使各级近似解都能准确满足全部初边值条件。

Based upon Adomian decomposition method, we have studied Adomian double decomposition method in this paper. The initial term in Adomian decomposition method has been further decomposed, and modified inverse vector method is obtained. The efficiency of double decomposition method is verified by the comparison between double decomposition method and Adomian decomposition method for solving differential equations. The experimental results demonstrate that the Adomian double decomposition method is better than the Adomian decomposition method for solving initial and boundary partial differential equation problems.