On a method for solving a local boundary problem for a nonlinear stationary system with perturbations in the class of piecewise constant controls

2019 ◽  
Vol 29 (13) ◽  
pp. 4515-4536
Author(s):  
Alexander N. Kvitko ◽  
Alla M. Maksina ◽  
Sergey V. Chistyakov
Keyword(s):  
Boundary Problem ◽  
Stationary System ◽  
Piecewise Constant ◽  
Local Boundary

scholarly journals Boundary problem with integral displacement for the model equation of elliptic type

2020 ◽  
pp. 65-74
Author(s):  
З.А. Нахушева
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problems ◽  
Boundary Problem ◽  
Model Equation ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Elliptic Type ◽  
Order Elliptic Equation ◽  
Local Boundary ◽  
Second Order Elliptic Equation

Для модельного эллиптического уравнения второго порядка рассматривается метод редукции нелокальных краевых задач с интегральным смещением к локальным краевым задачам для уравнения более высокого порядка составного типа. Исследуется разрешимость поставленных задач. For a model second order elliptic equation is considered the method of reduction of nonlocal boundary value problems with integral offset to the local boundary value problems for equations of higher order composite type. The solvability of tasks is investigated.

Local High-Accuracy Plate Analysis Using Wavelet-Based Multilevel Discrete-Continual Finite Element Method

2016 ◽  
Vol 685 ◽  
pp. 962-966 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva ◽  
Mojtaba Aslami ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Problem ◽  
High Accuracy ◽  
Geometrical Parameters ◽  
Wavelet Basis ◽  
Basic Direction ◽  
Piecewise Constant ◽  
Plate Analysis ◽  
Element Method

The distinctive paper is devoted to application of wavelet-based discrete-continual finite element method (WDCFEM), to analysis of plates with piecewise constant physical and geometrical parameters in so-called “basic” direction. Initial continual and discrete-continual formulations of the problem are presented. Due to special algorithms of averaging using wavelet basis within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem for system of ordinary differential equations is given.

Correct Wavelet-based Multilevel Discrete-Continual Methods for Local Solution of Boundary Problems of Structural Analysis

2013 ◽  
Vol 353-356 ◽  
pp. 3224-3227 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva
Keyword(s):  
Structural Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Problem ◽  
Local Solution ◽  
Wavelet Basis ◽  
Boundary Problems ◽  
Piecewise Constant ◽  
Constant Coefficients ◽  
Operational Formulation

The distinctive paper is devoted to correct wavelet-based multilevel discrete-continual methods for local solution of boundary problems of structural analysis. Initial discrete-continual operational formulation of the considering problem and corresponding operational formulation with the use of wavelet basis are presented. Due to special algorithms of averaging within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem of structural mechanics for system of ordinary differential equations with piecewise-constant coefficients is given.

scholarly journals Qualitative Study on Solutions of a Hadamard Variable Order Boundary Problem via the Ulam–Hyers–Rassias Stability

2021 ◽  
Vol 5 (3) ◽  
pp. 108
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Sina Etemad ◽  
Ali Hakem ◽  
Praveen Agarwal ◽  
...  
Keyword(s):  
Fixed Point ◽  
Qualitative Study ◽  
Boundary Value Problem ◽  
Boundary Problem ◽  
Fixed Point Theorems ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Piecewise Constant ◽  
The Given ◽  
Rassias Stability

In this paper, the existence, uniqueness and stability of solutions to a boundary value problem of nonlinear FDEs of variable order are established. To do this, we first investigate some aspects of variable order operators of Hadamard type. Then, with the help of the generalized intervals and piecewise constant functions, we convert the variable order Hadamard FBVP to an equivalent standard Hadamard BVP of the fractional constant order. Further, two fixed point theorems due to Schauder and Banach are used and, finally, the Ulam–Hyers–Rassias stability of the given variable order Hadamard FBVP is examined. These results are supported with the aid of a comprehensive example.

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