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时间分数阶四阶扩散方程的显-隐和隐-显差分格式

刘新龙, 杨晓忠   

  1. 华北电力大学数理学院, 北京 102206
  • 收稿日期:2019-08-29 出版日期:2020-09-15 发布日期:2020-09-15
  • 通讯作者: 杨晓忠,yxiaozh@ncepu.edu.cn.
  • 基金资助:

    国家科技重大专项子课题(No.2017ZX07101001-01)和国家自然科学基金项目(No.11371135).

刘新龙, 杨晓忠. 时间分数阶四阶扩散方程的显-隐和隐-显差分格式[J]. 数值计算与计算机应用, 2020, 41(3): 216-231.

Liu Xinlong, Yang Xiaozhong. EXPLICIT-IMPLICIT AND IMPLICIT-EXPLICIT DIFFERENCE SCHEMES FOR TIME FRACTIONAL FOURTH-ORDER DIFFUSION EQUATION[J]. Journal of Numerical Methods and Computer Applications, 2020, 41(3): 216-231.

EXPLICIT-IMPLICIT AND IMPLICIT-EXPLICIT DIFFERENCE SCHEMES FOR TIME FRACTIONAL FOURTH-ORDER DIFFUSION EQUATION

Liu Xinlong, Yang Xiaozhong   

  1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
  • Received:2019-08-29 Online:2020-09-15 Published:2020-09-15
时间分数阶四阶扩散方程是一类重要的发展型偏微分方程,其数值解的研究有重要的科学意义和工程实际价值.本文针对时间分数阶四阶扩散方程,研究一类显-隐(E-I)差分格式和隐-显(I-E)差分格式解法,该方法基于经典隐式和经典显式格式相结合构造而成,分析E-I和I-E两种差分格式解的存在唯一性、稳定性和收敛性.理论分析和数值试验结果证实本文E-I差分格式和I-E差分格式无条件稳定,具有空间2阶精度,时间2-α阶精度.在计算精度一致的要求下,E-I和I-E差分格式较经典隐式差分格式具有省时性,其计算时间相比古典隐格式减少约70%,研究表明本文格式求解时间分数阶四阶扩散方程是有效的.
Time fractional fourth-order diffusion equation is an important type of developmental partial differential equation and its numerical solution is of great scientific significance and practical value. In this paper, we study a class of explicit-implicit (E-I) difference schemes and implicit-explicit (I-E) difference schemes for time fractional fourth-order diffusion equation. The method is constructed by combining classical explicit scheme and classical implicit scheme. The existence and uniqueness and convergence of solutions are given for E-I and I-E difference schemes, Theoretical analysis and numerical experiments show that the E-I difference scheme and I-E difference scheme are unconditionally stable, with spatial 2 order spatial accuracy and time 2-α order temporal accuracy. Under the requirement of consistent calculation accuracy, the E-I and I-E difference schemes are more time-saving than the classical implicit difference scheme, and their calculation time is reduced by about 70% compared with the classical implicit difference scheme. Research shows that the schemes presented in this paper are effective for solving time fractional fourth-order diffusion equation.

MR(2010)主题分类: 

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