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.
Highlights
Holomorphic function was investigated with the help of complex analysis, which dealt with branch of the mathematics
This paper is focused on the Dirichlet eigenvalue problem
Various eigenvalue problems were summarized in this paper along with eigen function for them
Summary
Holomorphic function was investigated with the help of complex analysis, which dealt with branch of the mathematics. The function from the complex region or plane having the complex values falls in the category of holomorphic function. Differentiation of complex terms is more difficult than the real or normal differentiation. The function is defined in a set of complex or real values termed as bounded. The Integral equation for the boundary along with its numerical approximation is popular in variety fields for eg. Helmholtz equation gives the model of scattering phenomena having appropriate conditions in presence of scattered field. There is different reformulations are observed in form of integral equation on scattering object surface
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