A high-order numerical scheme for the impulsive fractional ordinary differential equations. Issue 12 (2nd December 2018) - Cao, Junying
ABSTRACT: In this paper, we use a good technique to construct a high-order numerical scheme for the impulsive fractional ordinary differential equations (IFODEs). This technique is based on the so-called block-by-block method, which is a common method for the integral equations. In our approach, the classical block-by-block method is improved so as to avoid the coupling of the unknown solutions at each block step with an exception in the first two steps between two adjacent pulse points. The convergence and stability analysis of the scheme are given. It proves that the numerical solution converges to the exact solution with order 3+ q for0 < q ≤ 1, where q is the order of the fractional derivative. A series of numerical examples are provided to support the theoretical results.