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微分方程的一些数值迭代解法

作　者: Abdul Wasim Shaikh
导　师: 程晓良
学　校: 浙江大学
专　业: 计算数学
关键词: 迭代解法微分方程博士学位论文指导教师计算数学浙江大学作者姓名论文题目培养单位数学系
分类号: O241.8
类　型: 博士论文
年　份: 2006年
下　载: 296次
引　用: 0次
阅　读: 论文下载

内容摘要

This thesis consists of three chapters. In chapter one, we give survey of the numerical methods for solving the diffusion equation subject to the specification of mass, numerical methods combining the numerical solutions of the equivalent integral equations with the backward implicit finite difference method, a numerical schemes for obtaining Pade approximant solutions to the initial boundary value problem for one-dimensional diffusion equation with non-local boundary condition, and efficient parallel technique for one-dimensional time-dependent diffusion equation with two non-local constraints. We include the research background and a brief introduction of diffusion equation. In the section 1.4 of this chapter, here we propose a penalty method for solving the diffusion equation subject to the specification of mass and obtain some error estimates. We also present some numerical results.In chapter two, we proposed a finite difference method and an iterative method for the L-Shape domain based on the domain decomposition method. We use the coarse mesh on the interface and fine mesh in the two domains. We derive the error estimates and have proved our iterative algorithm has a better convergence rate than the standard method.In chapter three, we introduced the iterative penalty method for the Stokes equations. We construct the iterative penalty algorithm to allow the use of not very small penalty parameter. We prove the error estimation and presented some numerical results to support our analysis.

全文目录

Abstract  4-5
Acknowledgements  5-6
Contents  6-8
Chapter. 1 The boundary penalty method for the diffusion equation subject to the specification of mass  8-57
  1.1. Introduction  8-10
  1.2 Background  10-13
  1.3 Techniques and Methods for Diffusion equation  13-44
    1.3.1 Galerkin Method  13-21
    1.3.2 Backward implicit finite difference method.  21-28
    1.3.3 Third-order Parallel algorithms (Splitting) method  28-37
    1.3.4 Numerical Technique on the Pade approximation  37-44
  1.4 The boundary penalty method for the diffusion equation  44-57
    1.4.1 Introduction  44-45
    1.4.2 The boundary penalty method  45-47
    1.4.3 Finite element method  47-54
    1.4.4 Numerical results  54-57
2 Iterative methods for the Poisson equation in L-shape domain based on domain decomposition method  57-66
  2.1 Introduction  57-58
  2.2 The Difference Scheme  58-61
  2.3 Iterative Method  61-65
  2.4 Numerical Experiments  65-66
Chapter. 3 Analysis of the iterative penalty method for the Stokes equations  66-71
  3.1 Introduction  66-67
  3.2 Error Estimates  67-70
  3.3 Numerical Test  70-71
Bibliography  71-77

微分方程的一些数值迭代解法

内容摘要

全文目录

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