Numerical solution of the singularly perturbed problem with nonlocal boundary condition

2002 ◽  
Vol 23 (7) ◽  
pp. 755-764 ◽  
Author(s):  
G. M. Amiraliyev ◽  
Musa Çakir
Keyword(s):  
Boundary Condition ◽  
Numerical Solution ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem

Numerical solution of hyperbolic-Schrödinger equations with nonlocal boundary condition

2012 ◽  
Author(s):  
Yildirim Ozdemir ◽  
Mehmet Kucukunal
Keyword(s):  
Boundary Condition ◽  
Numerical Solution ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary

scholarly journals Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Habtamu Garoma Debela
Keyword(s):  
Boundary Condition ◽  
Differential Equations ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Operator Method ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
Convection Diffusion ◽  
Fitted Operator

This paper presents the study of singularly perturbed differential equations of convection-diffusion type with nonlocal boundary condition. The proposed numerical scheme is a combination of the classical finite difference method for the boundary conditions and exponential fitted operator method for the differential equations at the interior points. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical examples considered. The method is shown to be first-order accuracy independent of the perturbation parameter ε .

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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