数学物理学报(英文版)

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AN IMPROVED SEARCH-EXTENTION METHOD FOR SOLVING SEMILINEAR PDES

谢资清; 陈传淼; 徐云   

  1. 湖南师范大学计算研究所, 长沙 410081
  • 收稿日期:2005-01-10 修回日期:1900-01-01 出版日期:2006-10-20 发布日期:2006-10-20
  • 通讯作者: 谢资清
  • 基金资助:

    This research was supported by the National Natural Science Foundation of China (10571053), Scientific Research Fund of Hunan Provincial Education Department (0513039), and the Special Funds of State Major Basic Research Projects (G1999032804)

AN IMPROVED SEARCH-EXTENTION METHOD FOR SOLVING SEMILINEAR PDES

Xie Ziqing; Chen Chuanmiao; Xu Yun   

  1. Institute of Computation, Hunan Normal University, Changsha 410081, China
  • Received:2005-01-10 Revised:1900-01-01 Online:2006-10-20 Published:2006-10-20
  • Contact: Xie Ziqing

摘要:

This article will combine the finite element method, the interpolated coefficient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilinear elliptic equations. This strategy not only grently reduces the expensive computation,
but also is successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems with non-odd nonlinearity on some convex or nonconvex domains. Numerical solutions illustrated by their graphics for visualization will show the efficiency of the approach.

关键词: Semilinear PDES, interpolated coefficient finite element method, multiple solutions, improved search-extension

Abstract:

This article will combine the finite element method, the interpolated coefficient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilinear elliptic equations. This strategy not only grently reduces the expensive computation,
but also is successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems with non-odd nonlinearity on some convex or nonconvex domains. Numerical solutions illustrated by their graphics for visualization will show the efficiency of the approach.

Key words: Semilinear PDES, interpolated coefficient finite element method, multiple solutions, improved search-extension

中图分类号: 

  • 65N30