三维热传导方程的一族两层显式格式

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基金项目: 福建省自然科学基金资助项目

A Class of Two-Level Explicit Difference Schemes for Solving Three Dimensional Heat Conduction Equation

Depertment of Management Information Science, Huaqiao University, Quanzhou, Fujian 362011, P R China

摘要: 提出了一族三维热传导方程的两层显式差分格式,当截断误差阶为O(Δt+(Δx)²)时,稳定性条件为网格比r=Δt/(Δx)²=Δt/(Δy)²=Δt/(Δz)²≤1/2,优于其他显式差分格式。而当截断误差阶为O((Δt)²+(Δx)⁴)时,稳定性条件为r≤1/6,包含了已有的结果。
- 三维热传导方程 /
- 显式差分格式 /
- 截断误差 /
- 稳定性
Abstract: A class of two-level explicit difference schemes are presented for solving three-dimensional heat conduction equation.When the order of truncation error is O(Δt+(Δx)²),the stability condition is mesh ratio r=Δt/(Δx)²=Δt/(Δy)²=Δt/(Δz)²≤1/2, which is better than that of a all the other explicit difference schemes.And when the order of truncation error is O((Δt)²+(Δx)⁴),the stability condition is r≤1/6,which contains the known results.
- three-dimensional heat conduction equation /
- explicit difference scheme /
- truncation error /
- stability condition

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