论文标题
混合型时间裂缝方程的紧凑型差异方案的尖端错误估计
Pointwise error estimates of compact difference scheme for mixed-type time-fractional Burgers' equation
论文作者
论文摘要
在本文中，基于开发的非线性四阶操作员和减少订单的方法，为混合型时级汉堡方程式建造了一种新颖的四阶紧凑型差异方案，从中，$ l_1 $ discretization complization用来处理分数衍生派的术语，而不是散发术语的术语。然后，可以通过与经典紧凑型差异公式近似空间二阶导数来确定完全离散的紧凑型差异方案。通过能量参数和数学诱导，在$ l^{\ infty} $中严格证明了收敛性和稳定性。最后，提供了一些数值实验来验证理论分析。
In this paper, based on the developed nonlinear fourth-order operator and method of order reduction, a novel fourth-order compact difference scheme is constructed for the mixed-type time-fractional Burgers' equation, from which $L_1$-discretization formula is employed to deal with the terms of fractional derivative, and the nonlinear convection term is discretized by nonlinear compact difference operator. Then a fully discrete compact difference scheme can be established by approximating spatial second-order derivative with classic compact difference formula. The convergence and stability are rigorously proved in the $L^{\infty}$-norm by the energy argument and mathematical induction. Finally, several numerical experiments are provided to verify the theoretical analysis.
