Abstract
In this paper, we present a superlinear numerical method for multi-term fractional nonlinear ordinary differential equations (MTFNODEs). First, the presented problem is equivalently transformed into its integral form with multi-term Riemann–Liouville integrals. Second, the compound product trapezoidal rule is used to approximate the fractional integrals. Then, the unconditional stability and convergence with the order [Formula: see text] of the proposed scheme are strictly established, where [Formula: see text] and [Formula: see text] are the maximum and the second maximum fractional indexes in the considered MTFNODEs, respectively. Finally, two numerical examples are provided to support the theoretical results.
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