The Implicit Difference Scheme of Eight Points for Solving the Parabolic Equations

Zhou Min; Gao Xue-jun; Dong Chao

doi:10.3969/j.issn.1007-7162.2014.04.013

English Version Journal Login

您当前的位置：

首页 >

文章列表页 >

The Implicit Difference Scheme of Eight Points for Solving the Parabolic Equations

更新时间：2026-05-27

- The Implicit Difference Scheme of Eight Points for Solving the Parabolic Equations
- Vol. 31, Issue 4, Pages: 69-73(2014)
- 作者机构：
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.1007-7162.2014.04.013
  CLC：
- Online First：28 December 2014，
  
  Published：2014
- 稿件说明：
移动端阅览
周敏, 高学军, 董超. 解抛物型方程的八点隐式差分格式[J]. 广东工业大学学报, 2014, 31(4): 69-73.

Zhou Min, Gao Xue-jun, Dong Chao. The Implicit Difference Scheme of Eight Points for Solving the Parabolic Equations[J]. 2014, 31(4): 69-73.
周敏, 高学军, 董超. 解抛物型方程的八点隐式差分格式[J]. 广东工业大学学报, 2014, 31(4): 69-73. DOI： 10.3969/j.issn.1007-7162.2014.04.013.

Zhou Min, Gao Xue-jun, Dong Chao. The Implicit Difference Scheme of Eight Points for Solving the Parabolic Equations[J]. 2014, 31(4): 69-73. DOI： 10.3969/j.issn.1007-7162.2014.04.013.

摘要

针对一维抛物型方程的初边值问题

在网格剖分的基础上

先用待定系数法构造出了一个含有多个参数的差分格式

然后利用Taylor级数展开法，并结合偏微分方程本身的特性在

、

处展开

使其达到一定的精度

最后解方程确定参数. 按照这样的方法

构造了一个两层八点隐式差分格式

其格式的截断误差为O(τ

)

稳定性条件是0.001

0.231或0.236

0.772

并给出了相应的数值算例验证了方法的可行性和有效性.

Abstract

Solutions to the initial boundary value problem with onedimension parabolic equations were presented. On the basis of mesh，an implicit difference scheme with multiple variables was given by the undetermined parameters method. Then

it was expanded with Taylor series by combining the characteristics of partition differential equations in

、

to reach certain accuracy. Finally

parameters of the equation were determined. Via this method

an implicit difference scheme of two layers and eight points for solving parabolic equation was constructed. The order of truncation error was O(τ

)

and the stability condition was 0.001

0.231 or 0.236

0.772. The corresponding numerical example has been given to

demonstrate the feasibility and effectiveness of the proposed method.

关键词

Keywords

references

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

The Cross-twin Physics-informed Neural Network for Wave Equations with Conserved Quantities

Bimodal Iterative Cross-attention Fusion Ensemble Framework

Research and Implementation of a Pulsed Laser Ranging Method Based on Digital Mixing

Robust Design for Artificial Noise-assisted UAV Terahertz Secure Communication

Energy Management Strategy of Hybrid Locomotive Based on Road Condition Parameters

Related Author

No data

Related Institution

No data

AI问答

⁰