时间分数阶对流扩散方程的有限点法分析

Analysis of the Finite Point Method for the Time Fractional Convection-diffusion Equation

基于有限差分法得到时间离散格式和利用有限点法建立离散代数系统,提出了数值求解时间分数对流扩散方程的无网格有限点法,详细推导了时间离散格式是无条件稳定的和该方法的理论误差估计.数值算例验证了理论结果,并验证了该方法的有效性和收敛性.

With the finite difference method to obtain the time discrete scheme and by means of the finite point method to establish discrete algebraic equation systems,a meshless finite point method for the numerical analysis of the time fractional convective-diffusion equation is proposed.The time discrete scheme is unconditionally stable,and the error estimation of the method is derived and discussed in detail.Numerical examples verify the theoretical results,and the efficiency and convergence of the proposed method.