Adomian分解法求解非线性分数阶积分微分方程

Adomian decomposition method for solving nonlinear integro-differential equations of fractional order

求一类非线性分数阶Volterra积分微分方程数值解,给出了Adomian分解法.将Adomian多项式与分数阶积分定义有效结合,得到了Adomian级数解.收敛性分析证明了所得级数解收敛于精确解,并给出最大截断误差.结果表明:随着Adomian多项式个数的增加,数值解的精度也越来越高.数值算例表明了该方法的可行性和有效性.与已有的方法相比,Adomian分解法操作更有效、更方便.

In order to obtain the numerical solution of a class of nonlinear Volterra integro-differential equations of fractional order, a computational method is presented in this paper, which is based on Adomian decomposition method. Also, the Adomian series solution is obtained by combining the Adomian polynomials with the definition of fractional order integral. The convergence analysis shows that the series solution converges to the exact solution, and the maximum absolute truncated error of the Adomian series solution is also given. The results show that the more Adomian polynomials, the higher the precision of the numerical solution. Numerical example demonstrates the validity and applicability of the method presented. Comparing with the known approach, the method presented is more efficient and more convenient.