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Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (9): 1221-1230 .doi: https://doi.org/10.1007/s10483-008-0911-y

• Articles • 上一篇    下一篇

色散方程的一类新的高精度交替分组显隐算法

张青洁,王文洽   

  1. 山东大学 数学学院,济南 250100
  • 收稿日期:2007-11-20 修回日期:2008-08-01 出版日期:2008-09-10 发布日期:2008-09-10
  • 通讯作者: 王文洽

A new alternating group explicit-implicit algorithm with high accuracy for dispersive equation

ZHANG Qing-jie, WANG Wen-qia   

  1. School of Mathematics, Shandong University, Jinan 250100, P. R. China
  • Received:2007-11-20 Revised:2008-08-01 Online:2008-09-10 Published:2008-09-10
  • Contact: WANG Wen-qia

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摘要： 对于具有周期性边界条件的色散方程,提出了一种高精度的交替分组显隐格式新解法(nAGEI).它不但无条件稳定,而且同已有的ASEI和AGE等交替方法比较,还具有精度高、收敛快的特点,数值实验表明新方法关于空间步长具有四阶收敛速度.

关键词: 高阶精度, Dispersive方程, 有限差分, 交替分组显隐方法, 绝对稳定, 并行计算

Abstract: In this paper, a new alternating group explicit-implicit (nAGEI) scheme for dispersive equations with a periodic boundary condition is derived. This new unconditionally stable scheme has a fourth-order truncation error in space and a convergence ratio faster than some known alternating methods such as ASEI and AGE. Comparison in accuracy with the AGEI and AGE methods is presented in the numerical experiment.

Key words: alternating group explicit-implicit method (nAGEI), high accuracy, unconditional stability, parallel computation, Dispersive equation, finite difference

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