多项时间分数阶混合扩散-波动方程ADI有限差分法  

ADI Finite Difference Method for Multi-term Time Fractional Mixed Diffusion-Wave Equations

作　　者：黎丽梅[1] 易云玲 郭欣雨 郭广源 LI Limei;YI Yunling;GUO Xinyu;GUO Guangyuan(School of Mathematics,Hunan Institute of Science and Technology,Yueyang 414006,China)

机构地区：[1]湖南理工学院数学学院,湖南岳阳414006

出　　处：《湖南理工学院学报（自然科学版）》2024年第3期1-7,共7页Journal of Hunan Institute of Science and Technology(Natural Sciences)

基　　金：国家级大学生创新创业计划训练项目(202210543026)。

摘　　要：用交替方向隐式(ADI)有限差分法研究多项时间分数阶混合扩散-波动方程的数值解,在时间方向上,采用降阶的方法,将扩散项和波动项转化为RL积分项和扩散项,分别使用L2-1_(σ)和L1公式逼近;空间方向结合二阶中心差商离散,并通过数值算例验证差分格式的有效性.The alternating direction implicit(ADI)finite difference method is employed to investigate the numerical solutions of multi-term time fractional mixed diffusion-wave equations.In the time direction,the diffusion and wave terms are transformed into RL integral terms and approximated using specific formulas.The spatial direction is discretized using the central difference quotient of the second order,and the effectiveness of the difference scheme is confirmed through numerical examples.

关 键 词：多项时间分数阶混合扩散-波动方程 交替方向隐式法 有限差分法 

分 类 号：O241.82[理学—计算数学]