本文關(guān)鍵詞： 偏積分微分方程 拉普拉斯變換數(shù)值逆 線性有限元法 迭代法 非線性問題　出處：《湖南師范大學(xué)》2006年碩士論文　論文類型：學(xué)位論文

【摘要】： 本文研究兩個(gè)問題．第一個(gè)問題是在記憶材料的熱轉(zhuǎn)導(dǎo)、多孔粘彈性介質(zhì)的壓縮、動(dòng)態(tài)人口、原子反應(yīng)動(dòng)力學(xué)等問題中，常常碰到的拋物型積分微分方程。對于該種方程的數(shù)值求解，國外的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，國內(nèi)的陳傳淼、黃云清、徐大、湯濤、胡齊芽、張鐵等做了大量的研究，，他們大多采用有限元方法，樣條配置方法，有限差分方法以及譜配置方法。但本文采用的空間線性有限元，時(shí)間拉普拉斯變換數(shù)值逆卻很少有人涉及。 第二個(gè)問題是煉銅堆浸工藝中的浸潤面所滿足的一個(gè)擬線性橢圓方程，建立不同類型堆浸控制參數(shù)及速率計(jì)算的數(shù)學(xué)模式是國內(nèi)外都感興趣的問題，尤其是在數(shù)學(xué)上準(zhǔn)確描述出來顯得特別重要而迫切。本文先用差分法離散，再用逆Broyden秩1迭代法和牛頓迭代法分別近似計(jì)算。 主要結(jié)果如下： (1)給出一類偏積分微分方程空間線性有限元，時(shí)間拉普拉斯變換數(shù)值逆的全離散格式及數(shù)值例子。 (2)給出堆浸工藝中浸潤面的非線性問題逆Broyden秩1迭代法及數(shù)值例子。 (3)給出堆浸工藝中浸潤面的非線性問題牛頓迭代法及數(shù)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 貿(mào) 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.
【學(xué)位授予單位】：湖南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2006
【分類號】：O241.82

【共引文獻(xiàn)】

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本文編號：1500020