scholarly journals Nonlocal Boundary Conditions Are Applied to the Analysis of Curve Equations

2022 ◽  
Vol 16 ◽  
pp. 248-256
Author(s):  
Qingling Wang ◽  
Lingling Fang
Keyword(s):  
Boundary Conditions ◽  
Traditional Method ◽  
Solution Method ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Complex Curve ◽  
Equation Solution ◽  
Local Boundary ◽  
Non Local ◽  
Curve Equation

The traditional curve equation solution method has a low accuracy, so the non-local boundary conditions are applied to the curve equation solution. Firstly, the solution coordinate system is established, and then the key parameters are determined to solve the curve equation. Finally, the curve equation is solved by combining the non-local boundary conditions. The experiment proves that the method of this design is more accurate than the traditional method in solving simple curve equation or complex curve equation.

scholarly journals STRICTLY CONVERGENT ALGORITHM FOR AN ELLIPTIC EQUATION WITH NONLOCAL AND NONLINEAR BOUNDARY CONDITIONS

2012 ◽  
Vol 17 (1) ◽  
pp. 128-139 ◽  
Author(s):  
Karlis Birgelis ◽  
Uldis Raitums
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Radiative Heat ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Nonlinear Boundary Conditions ◽  
Local Boundary ◽  
Transfer Processes ◽  
Nonlocal Terms ◽  
Convergent Algorithm

The paper describes a formally strictly convergent algorithm for solving a class of elliptic problems with nonlinear and nonlocal boundary conditions, which arise in modeling of the steady-state conductive-radiative heat transfer processes. The proposed algorithm has two levels of iterations, where inner iterations by means of the damped Newton method solve an appropriate elliptic problem with nonlinear, but local boundary conditions, and outer iterations deal with nonlocal terms in boundary conditions.

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Jiang ◽  
Zhong Chen ◽  
Ning Hu ◽  
Yali Chen
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Reproducing Kernel ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Orthonormal Bases ◽  
Fractional Differential

AbstractIn recent years, the study of fractional differential equations has become a hot spot. It is more difficult to solve fractional differential equations with nonlocal boundary conditions. In this article, we propose a multiscale orthonormal bases collocation method for linear fractional-order nonlocal boundary value problems. In algorithm construction, the solution is expanded by the multiscale orthonormal bases of a reproducing kernel space. The nonlocal boundary conditions are transformed into operator equations, which are involved in finding the collocation coefficients as constrain conditions. In theory, the convergent order and stability analysis of the proposed method are presented rigorously. Finally, numerical examples show the stability, accuracy and effectiveness of the method.

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