Asymptotic approximation by entire functions in infinite domains

The article is devoted to the determination of second-order perturbations in rectangular coordinates and components of the body motion to be under study. The main difficulty in solving this problem was the choice of a system of differential equations of perturbed motion, the coefficients of the projections of the perturbing acceleration are entire functions with respect to the independent regularizing variable. This circumstance allows constructing a unified algorithm for determining perturbations of the second and higher order in the form of finite polynomials with respect to some regularizing variables that are selected at each stage of approximation. Special points are used to reduce the degree of approximating polynomials, as well as to choose regularizing variables. The problem of generation of an asymptotic approximation of the solution of a perturbed differential equation system is considered in the case where a bifurcation occurs in the “fast motions” equation when the parameter changes: two equilibrium positions merge, followed by a change in stability.

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Introduction to the Theory of Entire Functions

10.1016/s0079-8169(08)x6144-6 ◽

1973 ◽

Keyword(s):

Entire Functions

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Uniqueness of entire functions sharing a small function with its derivatives

Novi Sad Journal of Mathematics ◽

10.30755/nsjom.06109 ◽

2018 ◽

Vol 48 (1) ◽

pp. 33-45

Author(s):

Goutam Kumar Ghosh

Keyword(s):

Entire Functions ◽

Small Function

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3D simulation of emulsion flow using the boundary element method on the heterogeneous computational systems

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2012.1.028 ◽

2012 ◽

Vol 9 (1) ◽

pp. 142-146

Author(s):

O.A. Solnyshkina

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Three Dimensional ◽

Reynolds Numbers ◽

Problem Size ◽

Low Reynolds Numbers ◽

Infinite Domains ◽

The Matrix ◽

Computational Systems ◽

Element Method

In this work the 3D dynamics of two immiscible liquids in unbounded domain at low Reynolds numbers is considered. The numerical method is based on the boundary element method, which is very efficient for simulation of the three-dimensional problems in infinite domains. To accelerate calculations and increase the problem size, a heterogeneous approach to parallelization of the computations on the central (CPU) and graphics (GPU) processors is applied. To accelerate the iterative solver (GMRES) and overcome the limitations associated with the size of the memory of the computation system, the software component of the matrix-vector product

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