A computational approach based on finite difference scheme and a redefined extended B-spline functions is presented to study the approximate solution of time fractional advection diffusion equation. The Caputo time-fractional derivative and redefined extended B-spline functions have been used for the time and spatial discretization, respectively. The numerical scheme is shown to be $O(h^2+\mathrm{\Delta }{t}^{2-\alpha })$ accurate and unconditionally stable. The proposed method is tested through some numerical experiments involving homogeneous/non-homogeneous boundary conditions which concluded that it is more accurate than existing methods. The simulation results show superior agreement with the exact solution as compared to existing methods.

提出了一种基于有限差分格式和重新定义的扩展B样条函数的计算方法，以研究时间分数维对流扩散方程的近似解。Caputo时间分数导数和重新定义的扩展B样条函数已分别用于时间和空间离散化。数值方案显示为$Ø（H^2+\mathrm{\Delta }{Ť}^{2--\alpha }）$准确且无条件地稳定。通过一些涉及齐次/非齐次边界条件的数值实验对提出的方法进行了测试，得出的结论是，该方法比现有方法更准确。与现有方法相比，仿真结果显示出与精确解决方案的优异一致性。