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AN IMPROVED SEARCH-EXTENTION METHOD FOR SOLVING SEMILINEAR PDES

AN IMPROVED SEARCH-EXTENTION METHOD FOR SOLVING SEMILINEAR PDES
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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. 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.
出处 《Acta Mathematica Scientia》 SCIE CSCD 2006年第4期757-766,共10页 数学物理学报(B辑英文版)
基金 This research was supported by the National Natural Science Foundation of China (10571053) Scientific Research Fund of Hunan Provincial Education Department (0513039) the Special Funds of State Major Basic Research Projects (G1999032804)
关键词 Semilinear PDES interpolated coefficient finite element method multiple solutions improved search-extension Semilinear PDES, interpolated coefficient finite element method, multiple solutions, improved search-extension
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