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A high-order scheme for fractional ordinary differential equations with the Caputo-Fabrizio derivative. (English) Zbl 07172818
Summary: In this paper, we consider numerical solutions of fractional ordinary differential equations with the Caputo-Fabrizio derivative, and construct and analyze a high-order time-stepping scheme for this equation. The proposed method makes use of quadratic interpolation function in sub-intervals, which allows to produce fourth-order convergence. A rigorous stability and convergence analysis of the proposed scheme is given. A series of numerical examples are presented to validate the theoretical claims. Traditionally a scheme having fourth-order convergence could only be obtained by using block-by-block technique. The advantage of our scheme is that the solution can be obtained step by step, which is cheaper than a block-by-block-based approach.
##### MSC:
 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 34A08 Fractional ordinary differential equations and fractional differential inclusions 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
FODE
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