An effective adaptive algorithm for linear fractional dynamical systems

This study proposes a time-stepping [Formula: see text] scheme to approximate the linear fractional dynamical systems based on nonuniform mesh. The developed numerical scheme is unconditionally stable, and exhibits second-order accuracy when the suitable graded mesh is used. A posteriori error estimation is derived for the obtained numerical scheme and the corresponding adaptive algorithm is devised. Finally, two numerical examples are provided to demonstrate the effectiveness of our approach and verify the theoretical results.