关键词: 二次样条插值, 分数阶子扩散方程, 超收敛性

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