Adomian分解法求二维非线性Volterra积分方程数值解

Adomian decomposition method for solving numerical solution to nonlinear two-dimensional Volterra integral equations

针对一类二维非线性Volterra积分方程,提出Adomian分解法,用Adomian多项式代替非线性部分,进而得到Adomian级数解。同时讨论级数解的收敛性,证明该解在一定条件下是收敛的,并给出Adomian级数解的最大绝对截断误差。算例表明了该方法的可行性和有效性。

Based on Adomian Decomposition Method, a computational method for solving a class of nonlinear two dimensional Volterra integral equations is presented. The Adomian series solution is derived by using Adomian pol ynomials to represent nonlinear term. At the same time, the convergence of series solution is discussed. It is shown that the series solution is convergent in certain conditions. Then the maximum absolute truncated error of the Ado mian series solution is obtained. Finally, feasibility and effectiveness of the proposed Adomian Decomposition Method is shown by numerical examples.