Abstract: For the time fractional sub-diffusion equation with variable coefficients, a numerical method is presented, Along the time direction, this method is constructed by using the recursion formula which is obtained from the use of the Lagrange interpolation function, along the space direction, the quadratic spline interpolation functions are used as the basis functions, and the compact optimal quadratic spline collocation scheme is built. Theoretical analyses and numerical examples show that super-convergence in space can be achieved in the collocation points.

Key words: quadratic spline interpolation, fractional sub-diffusion equation, optimal convergence

摘要： 对于变系数的时间分数阶子扩散方程，提出了一种数值方法，该方法在时间方向使用由Lagrange插值函数所得的递推公式，在空间方向，利用二次样条插值函数做为基函数，构成了最优紧二次样条配置法。理论分析和数值例子证明了该方法在配置点处具有超收敛性。

关键词: 二次样条插值, 分数阶子扩散方程, 超收敛性