大理大学学报 ›› 2023, Vol. 8 ›› Issue (6): 20-23.

• 数学与计算机科学 • 上一篇    下一篇

求解二维声波方程的高精度Runge-Kutta方法

陈 丽1,朱兴文2,张朝元2*   

  1. 1.大理大学工程学院,云南大理 6710032.大理大学数学与计算机学院,云南大理 671003
  • 收稿日期:2023-06-30 出版日期:2023-06-15 发布日期:2023-06-26
  • 通讯作者: 张朝元,教授,E-mail: zcy_km@163.com。
  • 作者简介:陈丽,副教授,主要从事地震波方程的数值方法及波场模拟研究。
  • 基金资助:
    国家自然科学基金项目(416640054146400451809026);云南省地方本科高校基础研究联合专项资金项目(202001BA070001-0822017FH001-006);大理大学科研发展基金项目(FZ2023YB035;FZ2023YB039

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

Chen Li1Zhu Xingwen2 Zhang Chaoyuan2*   

  1. 1. College of EngineeringDali UniversityDaliYunnan 671003China 2. College of Mathematics and ComputerDali UniversityDaliYunnan 671003China
  • Received:2023-06-30 Online:2023-06-15 Published:2023-06-26

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。

关键词:

"> ">声波方程, NAD">算子, Runge-Kutta">方法, 误差分析, 稳定性条件

Abstract:

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 eighth-order staggered grid scheme the eighth-order NAD-RK algorithm has the smallest numerical error.

Key words:

"> acoustic wave equation">, NAD operator">, Runge-Kutta method">, error analysis">, stability condition

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