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竞争物种的分数阶对流-弥散方程组的有限元方法

Finite Element Solution to Fractional Advection- Dispersion Modle with Two Species
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摘要 描述种群增长的分数阶偏微分方程组一般没有解析解,有限元方法是进行数值模拟的有效途径.针对两个竞争物种的非线性分数阶对流-弥散方程组,先进行时间半离散,然后运用压缩映射原理证明变分解的局部存在唯一性,同时给出求解有限元解的一种迭代算法.数值实例表明三次有限元迭代算法的时空收敛阶分别为1和4. Nonlinear space- fractional differential equations（ SFDEs） have more and more important applications in population growth model of biology. In this article a time semi- discrete formula and an iteration algorithm for SFDEs are presented. Using fixed point theorem,existence and uniqueness results for corresponding variable problems are proven in fractional derivative spaces. Numerical example illustrates the FEM iteration algorithm has first and fourth convergence rate for time and space,respectively.
作者 吴红英
机构地区 怀化学院数学与计算科学学院
出处 《怀化学院学报》 2016年第5期10-14,共5页 Journal of Huaihua University
关键词 对流-弥散方程组 分数微分算子 存在唯一性 迭代算法 advection-dispersion equations fractional differential operations existence and uniqueness iteration algorithm
分类号 O175.14 [理学—基础数学] O175.22 [理学—基础数学]
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参考文献13

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怀化学院学报
2016年 第5期

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