• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文学位 >Three numerical schemes for solving nonlinear partial differential equations.
【24h】

Three numerical schemes for solving nonlinear partial differential equations.

机译：求解非线性偏微分方程的三种数值格式。

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

This dissertation is concerned with numerical solutions to steady state 2-dimensional nonlinear elliptical partial differential equations with Dirichlet boundary conditions in a rectangular region. Three numerical schemes discussed in this dissertation are the iterative method, Newton's method, and the shooting method. In general the shooting method is only applied in ordinary differential equations, not in partial differential equations. In order to apply the shooting method and the Newton's method in a nonlinear partial differential equation, the alternating direction procedure is applied. Details of how to apply these three schemes are discussed in this dissertation as well as the implementation and numerical experiments.; Numerical results show that the alternating direction shooting method and the alternating direction Newton's method performed better than the commonly used linearized iterative method. Moreover, the greatest advantage of using the alternating direction procedure on the shooting method and Newton's method is that the computation is totally parallel. Therefore, if a parallel computing were to be used, it could achieve greater speedup. However the shooting method suffers stability problems as in ordinary differential equations. One possible way in which instability may be conquered is the consideration of multiple shooting methods which is not the objective of this dissertation.
机译：本文研究的是在矩形区域内具有Dirichlet边界条件的稳态二维非线性椭圆偏微分方程的数值解。本文讨论的三种数值格式分别是迭代法，牛顿法和射击法。通常，射击方法仅适用于常微分方程，而不适用于偏微分方程。为了将射击方法和牛顿法应用于非线性偏微分方程，应用了交替方向程序。本文详细讨论了这三种方案的应用方法，以及实现和数值实验。数值结果表明，交变方向射击法和交变方向牛顿法的性能优于常用的线性化迭代法。此外，在射击方法和牛顿方法上使用交替方向过程的最大优点是计算是完全并行的。因此，如果使用并行计算，则可以实现更大的加速。然而，射击方法遇到了与常微分方程一样的稳定性问题。克服不稳定的一种可能方式是考虑多种射击方法，这不是本文的目的。

著录项

  • 作者

    Cheng, Kang-Ping.;

  • 作者单位

    The University of Alabama.;

  • 授予单位 The University of Alabama.;
  • 学科 Mathematics.
  • 学位 Ph.D.
  • 年度 2003
  • 页码 86 p.
  • 总页数 86
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学;
  • 关键词

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号