A Convergence Algorithm of Boundary Elements for the Laplace Operator's Dirichlet Eigenvalue Problem

Abstract

A partial differential equation has been using the various boundary elements techniques for getting the solution to eigenvalue problem. A number of mathematical concepts were enlightened in this paper in relation with eigenvalue problem. Initially, we studied the basic approaches such as Dirichlet distribution, Dirichlet process and the Model of mixed Dirichlet. Four different eigenvalue problems were summarized, viz. Dirichlet eigenvalue problems, Neumann eigenvalue problems, Mixed Dirichlet-Neumann eigenvalue problem and periodic eigenvalue problem. Dirichlet eigenvalue problem was analyzed briefly for three different cases of value of λ. We put the result for multinomial as its prior is Dirichlet distribution. The result of eigenvalues for the ordinary differential equation was extrapolated. The Basic mathematics was also performed for λ calculations which follow iterative method.