2021年 02期

摘要(Abstract)：

为了数值求解一类多项分数阶非线性微分方程,构造一种具有一阶精度的显式数值方法;采用Riemann-Liouville积分算子,将多项分数阶非线性微分方程转化成与之等价的积分形式;基于该积分方程,运用复合矩形求积公式,给出有效的数值方法;对于2种不同形式的多项分数阶非线性微分方程,分别证明所构造数值方法的收敛性和无条件稳定性;通过3个数值算例,对数值方法进行验证。结果表明,该数值方法与理论计算结果相吻合,并且具有较高的计算效率。

关键词(KeyWords)： 多项分数阶非线性微分方程;数值方法;收敛性;稳定性;Riemann-Liouville积分

基金项目(Foundation): 国家自然科学基金项目(11701502)

作者(Author): 乔智,赵维加,黄健飞

DOI: 10.13349/j.cnki.jdxbn.20201010.003

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