（畢業(yè)論文）-熱傳導方程初邊值問題的差分解法

1、畢業(yè)論文 畢業(yè)論文(設計 設計)題 目: 熱傳導方程初邊值問題的差分解法 熱傳導方程初邊值問題的差分解法 院 ( 系 ): 數(shù)學與計算機科學學院 數(shù)學與計算機科學學院 _ 專業(yè)年級 專業(yè)年級: 2008 2008 級數(shù)學與應用數(shù)學系 級數(shù)學與應用數(shù)學系 姓 名: XXX XXX __ __ _ 學 號: 200808101134 200808101134 __ __

2、 _ 指導教師 指導教師: XXX______ XXX______ _ 2012 年 5 月AbstractThe article aims to explore the heat conduction equation initial boundary value problem of the finite difference method.This paper includes the following t

3、wo parts of the main content:The first part is compared with the traditional heat conduction equation initial boundary value problem of the separation of variables method finite difference method;The second part is the h

4、eat conduction equation initial boundary value problem of difference methods for specific examples.Which mainly relates to a method for heat conduction equation initial boundary value problem of the separation of variabl

5、es method and finite difference method. It first introduces the finite difference method. The basic idea is to use a continuous solution region using finite discrete points constitute a grid to replace, the discrete poi

6、nts are called grid node; the continuous solution of continuous variable function is used in the grid defined on a discrete variables function to approximate; the original equations and boundary conditions of the differe

7、nce quotient to micro commercial approximation, integral integral and to approximate, and the differential equations and boundary conditions is approximately replaced by algebraic equations, finite difference equation,

8、the solution to this equation can get the original problem in the discrete points on the approximate solution. And then using interpolation methods can be determined from the discrete solution solution of the approxima

9、te solution on the entire region. In the use of numerical methods for solving partial differential equations, if every derivative by finite difference approximation formula substitution, the solution of partial d

10、ifferential equations of the problem is transformed into solving algebraic equations, the so-called finite difference method.Finite difference method for solving partial differential equations:1discrete regions, w

11、hich are for solving partial differential equations by the finite region is subdivided into a lattice grid consisting of; 2approximate substitution, i.e. finite difference formula one substitution per lattice points of

12、 the derivative;3approximation solution. In other words, this process can be viewed as a polynomial interpolation and its differential instead of partial differential equation solution process. In contrast with the meth