关键词: 分数阶微分方程组, Caputo导数算子, 残差函数, 误差方程, 谱延迟校正法

Abstract: A spectral deferred correction method for classical ordinary differential equations is extended and reconstructed to solve a system of fractional differential equations (FDES) by accelerating the convergence of lower order schemes. Based on the residual function and the error equation deduced from Volterra integral equations equivalent to the fractional differential equations, a new high order numerical method for a system of FDES is constructed according to the idea of spectral deferred correction. The proposed method allows that one can use a relatively few nodes to obtain the high accuracy numerical solutions of FDES without the penalty of a huge computational cost due to the non-locality of Caputo derivative. The numerical experiments verify the high accuracy and efficiency of the method.

Key words: system of fractional differential equations, Caputo derivative, residual function, error equation, spectral deferred correction method