摘要
We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative.The method is developed by dividing the domain into a number of subintervals,and applying the quadratic interpolation on each subinterval.The method is shown to be unconditionally stable,and for general nonlinear equations,the uniform sharp numerical order 3−νcan be rigorously proven for sufficiently smooth solutions at all time steps.The proof provides a gen-eral guide for proving the sharp order for higher-order schemes in the nonlinear case.Some numerical examples are given to validate our theoretical results.
基金
This research was supported by National Natural Science Foundation of China(Nos.11901135,11961009)
Foundation of Guizhou Science and Technology Department(Nos.[2020]1Y015,[2017]1086)
The first author would like to acknowledge the financial support by the China Scholarship Council(201708525037)
The second author was supported by the Academic Research Fund of the Ministry of Education of Singapore under grant No.R-146-000-305-114.
