| Meshless methods is also said element-free methods. From the1990s to today, themeshless(or meshfree) has been a hot direction and the development trend of numerationfor science and engineering problems in recent years. But its development is not matureyet. No matter from mathematical theory and the application in engineering perspectives,they have many problems of no solution. As a new kind of numerical methods, therewas a little investigation on corrsponding mathematical theory for meshless methods, Itsconvergence, error estimation and other aspects of the research are still not perfect. Sothe application of meshless is certain restricted.The dissertation reviews the recent developments of the meshless methods by meansof their discretization scheme, together with some comments on the advantages and someexisting problems are to be further studied. Some of the papers also introduce the eigen-problems of theoretical knowledge and solving methods of eigenvalue problems. Based onthose, the meshless Galerkin and meshless collocation algorithm for eigenvalue problemsof compact integral operators are put forward in this paper.In second chapter,the solving method of eigen-problems is introduced. Power method,inverse power methods, Rayleign accelerated methods and Amended Rayleign acceleratedmethods of the eigen-problems of matrix methods and corresponding examples are given.In the third chapter gives some theoretical knowledge of projection approximation method. In fourth chapter,first, the basic principle of the moving least-square method(MLS) andthe error approximate estimate are given. Then, the paper introduces the the meshlessGalerkin algorithm for eigenvalue problems of compact integral operators and the erroranalysis and then gives some of their concrete proofs. At the last of this chapter putforward with meshless collocation method to solve eigenvalue problems, established bythis method in the feature vector and error estimation of eigen-problems. |
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