Coimbra变时间分数阶扩散-波动方程的新隐式差分法  

On a New Implicit Difference Method for Coimbra Variable Order Time Fractional Diffusion-Wave Equation

作　　者：马亮亮[1] 刘冬兵[1] 

机构地区：[1]攀枝花学院数学与计算机学院,四川攀枝花617000

出　　处：《西南师范大学学报（自然科学版）》2015年第3期25-31,共7页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(10671132;60673192);四川省科技厅资助项目(2013JY0125);攀枝花市市级应用技术研究与开发资金项目(2014CY-G-22);攀枝花学院校级培育项目(2012PY08);攀枝花学院校级科研项目(2013YB05;2012YB21);攀枝花学院院级科研创新项目(Y2013-04);攀枝花学院教育教学研究与改革青年项目(JJ1376)

摘　　要：将一阶的时间偏导数用Coimbra变时间分数阶导数算子进行替换,提出了一种新隐式差分解法.首先,对Coimbra型变时间分数阶导数算子和二阶空间导数进行离散化处理,将Coimbra变时间分数阶扩散-波动方程转化为代数方程组求解;然后,借助于数学归纳法给出了新隐式差分方法的收敛性分析,并证明了新隐式差分方法是无条件收敛的;最后,通过数值例子检验该方法,计算结果表明新隐式差分方法的理论分析是正确的,所构造的离散格式是可行的和有效的.In this paper ,a Coimbra variable order time fractional diffusion-wave equation has been consid-ered ,in w hich the first order derivative is replaced by a Coimbra variable order time fractional derivative operator ,and a new implicit difference method is given .Firstly ,the Coimbra variable order time fractional derivative and the second order space derivative is discretized and used to transform the Coimbra variable order time fractional diffusion-wave into a system of algebraic equations .Then ,the convergence of the new implicit difference method has been discussed by mathematical induction ,and it proves that the meth-od is unconditional stable .Finally ,a numerical example show s that the numerical analysis is right and the method is feasible and efficient .

关 键 词：分数阶扩散 波动方程 Coimbra变时间分数阶导数 收敛性 稳定性 数值解 新隐式差分格式 

分 类 号：O241.82[理学—计算数学]