论文标题
一种基于牛顿插值的预测 - 矫正器数值方法，用于分数微分方程，具有激活剂抑制剂案例研究
A Newton interpolation based predictor-corrector numerical method for fractional differential equations with an activator-inhibitor case study
论文作者
论文摘要
本文提出了一种适用于分数微分方程的新预测式数值方案。通过考虑被忽视的术语并用作所提出方法的预测阶段，获得了改进的显式Atangana-Seda公式。提出了数字公式，该公式近似于经典的第一衍生物以及Caputo，Caputo-Fabrizio和Atangana-Baleanu分数衍生物。模拟结果用于评估各种微分方程的新方法的近似误差。此外，考虑了一个案例研究，其中建议的方案用于获得Gierer-Meinhardt激活剂抑制剂模型的数值解，目的是评估系统的动力学。
This paper presents a new predictor-corrector numerical scheme suitable for fractional differential equations. An improved explicit Atangana-Seda formula is obtained by considering the neglected terms and used as the predictor stage of the proposed method. Numerical formulas are presented that approximate the classical first derivative as well as the Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. Simulation results are used to assess the approximation error of the new method for various differential equations. In addition, a case study is considered where the proposed scheme is used to obtained numerical solutions of the Gierer-Meinhardt activator-inhibitor model with the aim of assessing the system's dynamics.
