【作者】 吴专保；

【导师】 徐大；

【作者基本信息】 湖南师范大学 ， 基础数学， 2006， 硕士

【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。更多还原

【Abstract】 In this paper, we study two questions. The first is the integro-differential equation of parabolic type often occurs in applications such as heat conduction in material with memory, compression of poro-viscoelastic media, population dynamics, nuclear reactor dynamics, etc.. There are lots of documents of V. Thomée[1、5、7、16、17、18、19、20、21、22、23、24、31], Stig. Larsson [19], W. Mclean [5、17、20、24], Ch. Lubich[18], J. C. López-Marcos [14], J. M. Sanz-Serna [6], G. Fairweather[3、15], L. Wahlbin [1、17、19], I. H. Sloan [7、18、22、23], Yanping Lin [31] in overseas and Chuan-miao Chen [1、35], Yun-qing Huang [2], Da Xu [8、9、10、11、12、13], Tao Tang [33], Qiya Hu [34], Tie Zhang [38] in home. A lot of them use FEM; Spline collocation methods; finite difference methods; Spectral collocation methods. But few of them make the linear equation of the linear finite element method in the direction of of x and the inversion technique for the laplace transform in the direction of t. The second is the quasilinear equation of elliptic type in application such as infiltrates surface of heap leaching process. All are interested in building mathematical models of different types of heap leaching rates and parameters. It is particularly important and urgent to describe particularly in mathematicacs. The artical presents the difference method first to obtain the discretization, and then applies single rank inverse Broyden iterative method and newton iterative method.Mam results follows:(1)Given the numerical experiments and the full discretization for the linear equation of the linear finite element method in the direction of of x and the inversion technique for the laplace transform in the direction of t;(2)Given the numerical experiments and Single Rank Inverse Broyden Iterative method for a Nonlinear Problems to Infiltrates Surface of Heap Leaching Process.(3)Given the numerical experiments and Newton Iterative method for a Nonlinear Problems to Infiltrates Surface of Heap Leaching Process.更多还原