scholarly journals Finite Difference Method for Hyperbolic Equations with the Nonlocal Integral Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Necmettin Aggez
Keyword(s):  
Space Variable ◽  
Hyperbolic Equations ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Variable Coefficients ◽  
Difference Schemes ◽  
Order Difference ◽  
One Dimensional ◽  
Nonlocal Integral Condition ◽  
Multidimensional Hyperbolic Equations

The stable difference schemes for the approximate solution of the nonlocal boundary value problem for multidimensional hyperbolic equations with dependent in space variable coefficients are presented. Stability of these difference schemes and of the first- and second-order difference derivatives is obtained. The theoretical statements for the solution of these difference schemes for one-dimensional hyperbolic equations are supported by numerical examples.

scholarly journals On stable high order difference schemes for hyperbolic problems with the Neumann boundary conditions

2019 ◽  
Vol 9 (1) ◽  
pp. 60-72 ◽  
Author(s):  
Ozgur Yildirim
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
Nonlocal Boundary ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Order Difference

In this paper, third and fourth order of accuracy stable difference schemes for approximately solving multipoint nonlocal boundary value problems for hyperbolic equations with the Neumann boundary conditions are considered. Stability estimates for the solutions of these difference schemes are presented. Finite difference method is used to obtain numerical solutions. Numerical results of errors and CPU times are presented and are analyzed.

On a Nonlocal Boundary-value Problem for Two-dimensional Elliptic Equation

2001 ◽  
Vol 3 (1) ◽  
pp. 62-71
Author(s):  
Givi Berikelashvili ◽  
Nikolai I. Ionkin ◽  
Valentina A. Morozova
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Weighted Sobolev Space ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Two Dimensional ◽  
Averaging Operators ◽  
Nonlocal Integral Condition ◽  
Constant Coefficients

AbstractA boundary-value problem with a nonlocal integral condition is considered for a two-dimensional elliptic equation with constant coefficients and a mixed derivative. The existence and uniqueness of a weak solution of this problem are proved in a weighted Sobolev space. A difference scheme is constructed using the Steklov averaging operators.

scholarly journals Stability of difference schemes for Bitsadze-Samarskii type nonlocal boundary value problem involving integral condition

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 1027-1047 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Elif Ozturk
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Difference Schemes ◽  
Nonlocal Boundary Value Problem ◽  
Stability Of Difference Schemes ◽  
Gauss Elimination ◽  
Accuracy Difference ◽  
Gauss Elimination Method

In this study, the stable difference schemes for the numerical solution of Bitsadze-Samarskii type nonlocal boundary-value problem involving integral condition for the elliptic equations are studied. The second and fourth orders of the accuracy difference schemes are presented. A procedure of modified Gauss elimination method is used for solving these difference schemes for the two-dimensional elliptic differential equation. The method is illustrated by numerical examples.

scholarly journals Investigation of the spectrum of the Sturm–Liouville problem with a nonlocal integral condition

2013 ◽  
Vol 54 ◽  
pp. 67-72
Author(s):  
Agnė Skučaitė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Integral Condition ◽  
Characteristic Functions ◽  
Integral Type ◽  
Complex Characteristic ◽  
Nonlocal Integral Condition ◽  
Sturm Liouville

This paper presents some new results on the spectrum for the second order dif-ferential problem with one integral type nonlocal boundary condition (NBC). We investigate how the spectrum of this problem depends on the integral nonlocal boundary condition pa-rameters γ, ξ and the symmetric interval in the integral. Some new results are given on the complex spectra of this problem. Many results are presented as graphs of real and complex characteristic functions.

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