求解二维声波方程的高精度Runge-Kutta方法  

The High-Precision Runge-Kutta Method for Solving Two-Dimensional Acoustic Wave Equation

作　　者：陈丽 朱兴文 张朝元 Chen Li;Zhu Xingwen;Zhang Chaoyuan(College of Engineering,Dali University,Dali,Yunnan 671003,China;College of Mathematics and Computer,Dali University,Dali,Yunnan 671003,China)

机构地区：[1]大理大学工程学院,云南大理6671003 [2]大理大学数学与计算机学院,云南大理671003

出　　处：《大理大学学报》2023年第6期20-23,共4页Journal of Dali University

基　　金：国家自然科学基金项目(41664005,41464004,51809026);云南省地方本科高校基础研究联合专项资金项目(202001BA070001-082,2017FH001-006);大理大学科研发展基金项目(FZ2023YB035,FZ2023YB039)。

摘　　要：基于二维声波方程,结合八阶NAD算子离散空间高阶偏导数和三阶Runge-Kutta方法离散时间导数,发展了八阶NAD-RK算法。分析八阶NAD-RK算法的理论误差和数值误差,并详细推导了其稳定性条件。结果显示:同八阶Lax-Wendroff格式和八阶交错网格格式相比,八阶NAD-RK算法具有最小的数值误差。Based on the two-dimensional acoustic wave equation,the eighth-order NAD-RK algorithm is developed by combining the higher order partial derivative of the discrete space of the eighth-order NAD operator and the discrete time derivative of the third-order Runge-Kutta method.The theoretical and numerical errors of the eighth-order NAD-RK algorithm are analyzed,and its stability conditions are derived in detail.The results show that compared with the eighth-order Lax-Wendroff scheme and the eighthorder staggered grid scheme,the eighth-order NAD-RK algorithm has the smallest numerical error.

关 键 词：声波方程 NAD算子 RUNGE-KUTTA方法 误差分析 稳定性条件 

分 类 号：P631[天文地球—地质矿产勘探] O241[天文地球—地质学]