一个求解二维非线性时间分数阶波动方程的向后欧拉差分格式  

A Backward Euler Difference Scheme for Solving Two-Dimensional Nonlinear Time Fractional Wave Equations

作　　者：张光辉[1] ZHANG Guang-hui(School of Mathematics and Statistics,Suzhou University,Suzhou Anhui 234000,China)

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《菏泽学院学报》2023年第5期1-5,共5页Journal of Heze University

基　　金：安徽高校自然科学研究重点项目(KJ2021A1101,2022AH051370)。

摘　　要：基于所考虑方程的等价积分-微分形式,将卷积求积公式与向后欧拉差分公式相结合,建立了一种求解二维非线性时间分数阶波动方程的数值格式.通过理论推导说明该格式在时空方向上的精度为O(τ+h^(2)_(1)+h^(2)_(2)),并用数值算例验证了该结论.Based on the equivalent integral-differential form of the considered equation,this study combines the Convolution Quadrature Formula with the backward Euler Difference Scheme to establish a numerical scheme for solving two-dimensional nonlinear time fractional wave equations.The theoretical analysis demonstrates that the proposed scheme possesses a spatial-temporal accuracy of Numerical examples are provided to validate this conclusion.

关 键 词：时间分数阶 波动方程 卷积公式 欧拉差分 

分 类 号：O241.82[理学—计算数学]