非线性分数阶常微分方程组的Euler方法

Euler method for nonlinear systems of fractional ordinary differential equations

提出一种求解分数阶微分方程组的Euler方法。该方法基于Caputo导数的性质,将分数阶微分方程组转化为Volterra积分方程组,然后用Euler法求解Volterra积分方程组,并对方法的收敛性和稳定性做了证明。最后,给出数值例子,验证方法的有效性。

This paper presents a Euler method for solving fractional ordinary differential equations.The systems of fractional ordinary differential equations are transformed into Volterra integral equations by the properties of Caputo derivative,and the Volterra integral equations are solved by Euler methed.The convergence and stability of the method are proved.Finally,numerical examples are given to verify the effectiveness of the method.