两类偏微分方程的数值解

发布时间：2018-02-10 07:48

本文关键词： 偏积分微分方程拉普拉斯变换数值逆线性有限元法迭代法非线性问题　出处：《湖南师范大学》2006年硕士论文　论文类型：学位论文

【摘要】： 本文研究两个问题．第一个问题是在记忆材料的热转导、多孔粘弹性介质的压缩、动态人口、原子反应动力学等问题中，常常碰到的抛物型积分微分方程。对于该种方程的数值求解，国外的V．Thomée，Stig．Larsson，W．Mclean，C．Lubich，J．C．López-Marcos，J．M．Sanz-Serna，G．Fairweather，L．Wahlbin，I．H．Sloan，Yanping Lin等，国内的陈传淼、黄云清、徐大、汤涛、胡齐芽、张铁等做了大量的研究，，他们大多采用有限元方法，样条配置方法，有限差分方法以及谱配置方法。但本文采用的空间线性有限元，时间拉普拉斯变换数值逆却很少有人涉及。第二个问题是炼铜堆浸工艺中的浸润面所满足的一个拟线性椭圆方程，建立不同类型堆浸控制参数及速率计算的数学模式是国内外都感兴趣的问题，尤其是在数学上准确描述出来显得特别重要而迫切。本文先用差分法离散，再用逆Broyden秩1迭代法和牛顿迭代法分别近似计算。主要结果如下： (1)给出一类偏积分微分方程空间线性有限元，时间拉普拉斯变换数值逆的全离散格式及数值例子。 (2)给出堆浸工艺中浸润面的非线性问题逆Broyden秩1迭代法及数值例子。 (3)给出堆浸工艺中浸润面的非线性问题牛顿迭代法及数值例子。
[Abstract]:Two problems are studied in this paper. The first problem is the thermal transduction of memory materials, the compression of porous viscoelastic media, the dynamic population, the dynamics of atomic reaction, etc. Numerical solution of the parabolic integro-differential equation. For the numerical solution of this kind of equation, a lot of research has been done on the numerical solution of the equation by V. Thom 茅 eau Stig.Larssonn W. Mcleanen C. Lubichn J.C.L 贸 pez-Marcosi J. M. Sanz-Sernav G. Fairweatherer L.Wahlbinnberg, I. H. SloanYanping Lin et al., Chen Chuanmiao, Huang Yunqing, Xu Da, Tang Tao, Hu Qi-ya and Zhang tie, etc. Most of them use finite element method, spline collocation method, finite difference method and spectral collocation method, but the spatial linear finite element method and time Laplace transform numerical inversion are seldom discussed in this paper. The second problem is a quasilinear elliptic equation satisfied by the wetting surface in copper heap leaching process. It is of great interest to establish mathematical models for calculating the control parameters and rates of different types of heap leaching at home and abroad. In this paper, the difference method is used first, then the inverse Broyden rank 1 iteration method and the Newton iteration method are used to approximate the calculation, respectively. The main results are as follows:. In this paper, we give the full discrete scheme and numerical examples of linear finite element and time Laplace transform numerical inversion for a class of partial integrodifferential equations. The inverse Broyden rank 1 iteration method and numerical example are given for the nonlinear problem of infiltration surface in heap leaching process. In this paper, Newton iteration method and numerical example are given for the nonlinear problem of soakage surface in heap leaching process.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2006
【分类号】：O241.82

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