摘要
提出了非线性分数阶常微分方程初值问题的一种显式算法。首先将问题转化为等价的第二类Volterra积分方程,其次利用经典的Adams外插公式构造了一种收敛的显式算法,然后对该算法进行了收敛性和稳定性分析。最后,给出了数值算例,验证了方法的有效性。
In this paper,an explicit algorithm for the initial value problem of nonlinear fractional ordinary differential equations is proposed.Firstly,the fractional ordinary differential equations is transformed into the second equivalent Volterra integral equation.Seeondly,the numerical scheme is constructed by the integral equation in the classical Adams extrapolation formula.Then we carried out the convergence and stability analysis of the algorithm.Several numerical examples are provided to validate the theoretical results and to demonstrate the efficiency of the proposed method.
作者
周晓军
彭鑫
ZHOU Xiaojun;PENG Xin(School of Mathematical Science,Guizhou Normal University,Guiyang,Guizhou 550025,China)
出处
《贵州师范大学学报（自然科学版）》
CAS
2021年第6期13-19,共7页
Journal of Guizhou Normal University：Natural Sciences
基金
贵州师范大学博士科研项目(2016)。
作者简介
周晓军(1982-),男,博士,副教授,硕士生导师,研究方向:偏微分方程数值解法,E-mail:xjzhou@gznu.edu.cn.
