Adomian 分解法求解非线性分数阶 Volterra 积分方程

摘要

Application of Adomian decomposition method,series solution of nonlinear volterra integral equations of fractional order are approximately obtained. The equation is solved by combining Adomian polynomials with the defi-nition of fractional order integral. Convergence of the series solution is proved and the maximum absolute truncated error of the Adomian series solution is also given. Thus,the effectiveness and feasibility of the Adomian decomposi-tion method are illustrated by the numerical example.%Adomian 分解法求解非线性分数阶 Volterra 积分方程的数值解，将 Adomian 多项式与积分方程的定义相结合，得出一个递推公式求解方程的级数解，并进行了收敛性分析，给出了级数解的最大绝对截断误差，通过数值算例说明了该方法的有效性和可行性。