一维分数阶渗透方程的数值模拟  

NUMERICAL SIMULATION FOR THE ONE-DIMENSIONAL FRACTIONAL PERCOLATION EQUATION

作　　者：陈世平[1] 刘发旺 

机构地区：[1]泉州师范学院数学系,泉州362000 [2]澳大利亚昆土兰理工大学数学科学学院

出　　处：《高等学校计算数学学报》2010年第4期345-352,共8页Numerical Mathematics A Journal of Chinese Universities

基　　金：福建省教育厅A类科技项目(JA09211);国家自然科学基金资助项目(10271098和11001090)

摘　　要：渗流问题在水文、土壤、医学等许多研究领域被探讨.经典的整数阶渗透方程是在渗流连续的假设条件下建立的,但是这些假设在实际渗流中一般是不成立的,从而发展出能反映实际情况的分数阶渗透方程.In this paper,an one-dimensional fractional percolation equation with variable coefficients is considered.For solving the equation,it is decomposed to two simple fractional equations and numerical method is established respectively for them.Stability,consistency and convergence of the method are examined. Some numerical example with known exact solution is also presented to show the effective of the method.

关 键 词：渗透方程 分数阶 数值模拟 一维 渗流问题 整数阶 

分 类 号：O242.21[理学—计算数学]