Green’s functions for stationary problems with nonlocal boundary conditions

2009 ◽  
Vol 49 (2) ◽  
pp. 190-202 ◽  
Author(s):  
S. Roman ◽  
A. Štikonas
Keyword(s):  
Boundary Conditions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Stationary Problems

scholarly journals Linear ODE with nonlocal boundary conditions and Green’s functions for such problems

2019 ◽  
Vol 51 ◽  
pp. 379-384
Author(s):  
Svetlana Roman ◽  
Artūras Štikonas
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Linear Ode

In this article we investigate a formula for the Green’s function for the n-orderlinear differential equation with n additional conditions. We use this formula for calculatingthe Green’s function for problems with nonlocal boundary conditions.

scholarly journals The properties of Green’s functions for one stationary problem with nonlocal boundary conditions

2019 ◽  
Vol 50 ◽  
Author(s):  
Svetlana Roman ◽  
Artūras Štikonas
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Stationary Problem

In this paper we research Green’s function properties for stationary problem with four-pointnonlocal boundary conditions. Dependence of these functions on values ξ and γ is investigated. Green’sfunctions graphs with various values ξ and γ are presented.

scholarly journals Generalized Green’s functions for second-order discrete boundary-value problems with nonlocal boundary conditions

2012 ◽  
Vol 53 ◽  
pp. 96-101 ◽  
Author(s):  
Gailė Paukštaitė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Conditions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence Condition ◽  
Second Order ◽  
Linear Functionals ◽  
Discrete Green’S Function ◽  
Sufficient Existence Condition

In this paper, generalized Green’s functions for second-order discrete boundaryvalueproblems with nonlocal boundary conditions are investigated, where the necessaryand sufficient existence condition of discrete Green’s function is not satisfied and nonlocalboundary conditions are described by linear functionals.

scholarly journals Green functions for stationary problems with nonlocal boundary conditions

2008 ◽  
Vol 48 ◽  
pp. 333-337
Author(s):  
Svetlana Roman ◽  
Artūras Štikonas
Keyword(s):  
Boundary Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Green Functions ◽  
Classical Boundary ◽  
Stationary Problems

In this paper the Green functions for various stationary problems with nonlocal boundary conditions areinvestigated.We compare Green functions properties for classical boundary conditions with properties ofGreen functions for problems with nonlocal boundary conditions. Few examples iliustrate such properties.

scholarly journals STATIONARY PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS

2001 ◽  
Vol 6 (2) ◽  
pp. 178-191 ◽  
Author(s):  
R. Čiegis ◽  
A. Štikonas ◽  
O. Štikoniene ◽  
O. Suboč
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Difference Schemes ◽  
Maximum Norm ◽  
Finite Difference Schemes ◽  
Stability Estimates ◽  
Stationary Problems ◽  
Theoretical Results

In this article a stationary problems with general nonlocal boundary conditions is considered. The differential problems and finite difference schemes for solving this problem are investigated. Stability estimates are proved in the maximum norm and the non‐negativity of the solution is investigated. All theoretical results are illustrated by representative examples.

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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