Open AccessConstruction of the difference problem and error estimation of the approximate solution of the nonlocal problem for the nonlinear equation.
Author(s) -
A. Y. Aliyev,
Alovsat Aliyev,
J. К. Кazimov
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1451/1/012019
Subject(s) - mathematics , boundary value problem , nonlinear system , finite difference method , mathematical analysis , elasticity (physics) , finite difference , grid , linear elasticity , finite element method , geometry , physics , quantum mechanics , thermodynamics
In this paper, we consider a nonlocal problem. It is used in the rectangular area. For this problem, a difference problem is constructed, based on a rectangular grid. The error of theapproximatesolutionsfor a nonlocal problemis estimated. Many applied problems, in particular heat conductivity [1], [2], fluid mechanics [3], the theory of elasticity and shells [4], etc. are reduced to solving nonlocal boundary value problems for elliptical type equations. When solving nonlocal boundaryvalueproblems, nonlocal boundaryconditions complicate the justification of finite difference schemes due to the complexity of matrices obtained from systemsof equation.This complexity is especially evident for numerical methods, fornon-linear equations[5]. Here we consider a nonlocal boundary value problem for a quasi-linear equation. To solve the problem numerically we use the finite difference method. The error estimate of the approximate solution of the nonlocal problem is found.