In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step graded mesh procedure based on an expansion of the vector field using orthonormal Jacobi polynomials. Under mild hypotheses, the proposed procedure is capable of getting spectral accuracy. A few numerical examples are reported to confirm the theoretical findings.

翻译：本文研究分数阶微分方程的数值求解问题。具体而言，我们探索了一种基于标准正交雅可比多项式展开向量场的逐级分级网格方法。在温和假设条件下，该方法能够实现谱精度。若干数值算例被呈现以验证理论结果。