Finite Difference Methods for Elliptic Equations
Finite Difference Methods for Elliptic Equations
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DOI：
10.1007/978-3-540-88706-5_4
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发表时间：
2008-10
期刊：
影响因子：
--
通讯作者：
Jichun Li;Yitung Chen
中科院分区：
文献类型：
--
作者：
Jichun Li;Yitung Chen
偏微分方程数值分析的早期发展主要是由有限差分方法。在这种方法中，近似解是在有限点网格的点处寻求的，并且微分方程的近似是通过用适当的差分导数代替导数来完成的。这将微分方程问题简化为代数方程的有限线性系统。在这一章中，我们说明这两个点的边值问题在一维和Dirichlet问题的泊松方程在平面上。分析是基于前两章的最大值原理的离散版本。
The early development of numerical analysis of partial differential equations was dominated by finite difference methods. In such a method an approximate solution is sought at the points of a finite grid of points, and the approximation of the differential equation is accomplished by replacing derivatives by appropriate difference quotients. This reduces the differential equation problem to a finite linear system of algebraic equations. In this chapter we illustrate this for a two-point boundary value problem in one dimension and for the Dirichlet problem for Poisson’s equation in the plane. The analysis is based on discrete versions of the maximum principles of the previous two chapters.