The Analysis Of Finite Element Method And Parallel Algorithm With A Kind Of Singular Sturm-Liouville Problems

In history, Weyl.Hermann have researched the singular Sturm-Liouville problem first in 1910, has made the first important jobs in mathematics: The singular boundary condition of second order line differential equation. At present, the research to singular Sturm-Liouville problem is progressing unceasingly. Then, Some domestic and foreign scholars on the issue of different degrees of discussion. There are pertinent discussion to the incrementality and conformity of solution. The singular Sturm-Liouville problem having summarized in [20],have been discussed once in Courant and Hilbert's one book namely:Methods of Mathematical Physics Vol I.. Finding the solution to this problem , Chen Chuan-miao has studied finite element solution and high-accuracy theory of singular two-point boundary value problem. P.B.Bailey has discussed in [29] about the eigenvalue to singular Sturm-Liouville problem, and use Fortran language to have encrypted the corresponding procedure software package (be refer to [30]) that find the solution specifically for different types of singular endpoint. I discuss the singular Sturm-Liouville problem further in prehuman's research basis.It is an important problem having practical significance about the research to Sturm-Liouville problem. Especially finding the solution of singular Sturm-Liouville problem, there are practical significance to research singular Sturm-Liouville problem numerical solution. In view of that, find the solution of a kind of singular Sturm-Liouville problem by the finite element method and their parallel computing,the main body of thesis is that research the singular Sturm-Liouville problem further.The full text main works as follows:One, I have discussed the relations of a kind of the Three-dimensional eigenvalue problem and the singular Sturm-Liouville problem.Two, I has done Finite Element Method analysis to a kind of singular Sturm-Liouville problem and got the result being similar with common type Sturm-Liouville problem.I has used Matlab as numerical example that have testified these conclusions.Three, parallel computing the singular Sturm-Liouville problem based on net by two-grid method.