A third-order numerical method for solving fractional ordinary differential equations

• DOI: 10.3934/math.20241026
• Publication Date: 2024-07-01T10:45:01Z
• Authors: Xiaopeng Yi; Chongyang Liu; Huey Tyng Cheong; Kok Lay Teo; Song Wang
• Keywords: Algebraic equation

<p>In this paper, we developed a novel numerical method for solving general nonlinear fractional ordinary differential equations (FODEs). First, transformed the FODEs into equivalent Volterra integral equations. We then time-stepping algorithm solution of based on third-order Taylor expansion approximating integrands in chosen mesh with parameter $ h $. This approximation led to implicit algebraic unknowns at each given point, and an iterative Newton's was solve resulting A convergence analysis scheme showed that error between exact point is \mathcal{O}(h^{3}) $, independent order. Finally, four examples were solved verify theoretical results demonstrate effectiveness proposed method.</p>