分数阶扩散-波动方程数值求解

Numerical method for the fractional order diffusion-wave equation

针对Caputo分数阶导数意义下的时间分数阶扩散-波动方程进行数值研究.利用Caputo分数阶导数与Grunwald-Letnikov分数阶导数的关系对时间分数阶导数进行时间离散化处理,再利用二阶中心差商离散方程中的二阶空间导数,并结合边值条件的离散化,把离散化方程的求解转化为一个线性方程组的求解.利用Mat-lab编程实现了离散化方程组的求解,并绘制了不同参数下的数值解曲面.

Concerned with the numerical solving for the time fractional order diffusion-wave equation defined with the Caputo derivative.First by making use of the relation between the Caputo derivative and the Grunwald-Letnikov derivative,the time fractional derivatives can be discreted.Then the second-order space derivative in the equation is approximated by the second-order central difference quotient.Combined with the discretization of boundary value conditions,the solution of the discretization equations are transformed into linear equations＇ solution.Using Matlab programming to implement the above arithmetic,and draw the surface of numerical solution in different parameters.