求解分数阶延迟微分方程的卷积Runge-Kutta方法

Runge-Kutta Convolution Quadrature Methods for Solving Fractional Differential Equations with Delay

本文利用强A-稳定Runge-Kutta方法求解一类非线性分数阶延迟微分方程初值问题,并给出了算法的稳定性和误差分析.数值算例验证算法的有效性及其相关理论结果.

In this paper, a strongly A-stable Runge-Kutta method is constructed to solve a class of nonlinear fractional differential equation with delay and Caputo fractional derivative. Stability and error analysis of the numerical algorithm are given. Numerical experiments demonstrate the validity of the proposed numerical algorithm and related theoretical results.