Finite Difference Method
Finite Difference Method
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有限差分法
DOI：
10.1007/978-3-642-50319-1_3
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
Pei
中科院分区：
文献类型：
--
作者：
Pei
有限差分法是求解偏微分方程的一种近似方法。它被用来解决广泛的问题。这些问题包括线性和非线性，时间无关和相关问题。该方法可适用于不同边界形状、不同边界条件以及包含多种不同材料的区域的问题。尽管这种方法被高斯和玻尔兹曼等工作者所熟知，但直到20世纪40年代才被广泛用于解决工程问题。Richardson在1910年[1]已经知道了该方法的数学基础，并且出版了许多数学书籍，如参考文献[2和3]，其中讨论了有限差分法。关于电场和磁场问题的处理，在[4]中有具体的参考。有限差分法的应用并不困难，因为它在离散方程的推导和相应程序的编写中只涉及简单的算法。在1950-1970年期间，FDM是用于解决实际问题的最重要的数值方法（[5-7]）。随着具有大规模存储能力的高速计算机的发展，出现了许多求解偏微分方程的数值方法。然而，由于有限差分法应用方便，它仍然是解决这些问题的一种有价值的手段（[8-11]）。
The finite difference method (FDM) is an approximate method for solving partial differential equations. It has been used to solve a wide range of problems. These include linear and non-linear, time independent and dependent problems. This method can be applied to problems with different boundary shapes, different kinds of boundary conditions, and for a region containing a number of different materials. Even though the method was known by such workers as Gauss and Boltzmann, it was not widely used to solve engineering problems until the 1940s. The mathematical basis of the method was already known to Richardson in 1910 [1] and many mathematical books such as references [2 and 3] were published which discussed the finite difference method. Specific reference concerning the treatment of electric and magnetic field problems is made in [4]. The application of FDM is not difficult as it involves only simple arithmetic in the derivation of the discretization equations and in writing the corresponding programs. During 1950–1970 FDM was the most important numerical method used to solve practical problems ([5–7]). With the development of high speed computers having large scale storage capability many numerical solution techniques appeared for solving partial differential equations. However, due to the ease of application of the finite difference method it is still a valuable means of solving these problems ([8–11]).