基于非均匀网格的预测校正法求解非线性分数阶常微分方程初值问题
A Predictor-Corrector Method for Nonlinear Fractional Differential Equation Initial Value Problems on Graded Grids
摘要: 非线性分数阶微分方程初值问题的典型解在初始时刻具有弱奇异性，为了更好地逼近它的典型解，本文将Nguyen和Jang在均匀网格上的三阶预测校正方法推广到非均匀网格上。与文献中现有的预测校正方法相比，这种新方法在降低计算成本的同时，显著提高了数值精度。另外，通过数值算例得到的结果显示，当选择合适的网格参数时，误差的收敛阶大于3。
Abstract: In order to better approximate the classical solution of nonlinear fractional differential equation in-itial value problems, which has weak singularity at the initial time, the third order predictor- cor-rector method of Nguyen and Jang on uniform grids is extended to non-uniform grids. Compared with the existing predictor-corrector methods in the literature, this new method reduces the com-putation cost and significantly improves the numerical accuracy. In addition, numerical examples show that the convergence order of errors is greater than the third order when appropriate mesh parameters are selected.
文章引用：李一丹. 基于非均匀网格的预测校正法求解非线性分数阶常微分方程初值问题[J]. 应用数学进展, 2023, 12(12): 4907-4913. https://doi.org/10.12677/AAM.2023.1212483

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