scholarly journals Alternating direction method for two-dimensional parabolic equation with nonlocal integral condition

2012 ◽  
Vol 17 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Mifodijus Sapagovas ◽  
Kristina Jakubėlienė
Keyword(s):  
Parabolic Equation ◽  
Nonlocal Condition ◽  
Integral Condition ◽  
Rectangular Domain ◽  
Alternating Direction Method ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Alternating Direction ◽  
Nonlocal Integral Condition ◽  
Dimensional Domain

Two-dimensional parabolic equation with nonlocal condition is solved by alternating direction method in the rectangular domain. Values of the solution on the boundary points are bind with the integral of the solution in whole two-dimensional domain. Because of this nonlocal condition, the classical alternating direction method is complemented by the solution of low dimension system of algebraic equations. The peculiarities of the method are considered.

scholarly journals An eigenvalue problem for the differential operator with an integral condition

2012 ◽  
Vol 53 ◽  
Author(s):  
Kristina Jakubėlienė
Keyword(s):  
Parabolic Equation ◽  
Differential Operator ◽  
Eigenvalue Problem ◽  
Integral Condition ◽  
Stability Conditions ◽  
Two Dimensional ◽  
One Dimensional ◽  
Nonlocal Integral Condition

We analyze solution of a two-dimensional parabolic equation with a nonlocal integral condition by a locally one-dimensional method. The main aim of the paper is to deduce stability conditions of a system of one-dimensional equations with one integral condition. To this end, we analyze the structure of the spectrum of the differential operator with an integral condition.

Nonlinear nonlocal problems for a parabolic equation in a two-dimensional domain

1997 ◽  
Vol 49 (2) ◽  
pp. 269-280
Author(s):  
Yu. A. Mitropol’skii ◽  
A. A. Berezovskii ◽  
M. Kh. Shkhanukov-Lafishev
Keyword(s):  
Parabolic Equation ◽  
Two Dimensional ◽  
Nonlocal Problems ◽  
Dimensional Domain

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 ALTERNATING DIRECTION METHOD FOR A TWO-DIMENSIONAL PARABOLIC EQUATION WITH A NONLOCAL BOUNDARY CONDITION

2007 ◽  
Vol 12 (1) ◽  
pp. 131-142 ◽  
Author(s):  
Mifodijus Sapagovas ◽  
Gene Kairytė ◽  
Olegas Štikonienė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Alternating Direction Implicit Method ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Conditions Of Stability

The present paper deals with an alternating direction implicit method for a two dimensional parabolic equation in a rectangle domain with a nonlocal boundary condition in one direction. Sufficient conditions of stability for Peaceman‐Rachford method are established. Results of some numerical experiments are presented.

scholarly journals Numerical solution of nonlinear elliptic equation with nonlocal condition

2013 ◽  
Vol 18 (4) ◽  
pp. 412-426 ◽  
Author(s):  
Regimantas Čiupaila ◽  
Mifodijus Sapagovas ◽  
Olga Štikonienė
Keyword(s):  
Elliptic Equation ◽  
Nonlinear Elliptic Equation ◽  
Small Volume ◽  
Nonlocal Condition ◽  
Integral Condition ◽  
System Of Difference Equations ◽  
Differential Problem ◽  
Minimal Surface Equation ◽  
Nonlinear Elliptic ◽  
Nonlocal Integral Condition

Two iterative methods are considered for the system of difference equations approximating two-dimensional nonlinear elliptic equation with the nonlocal integral condition. Motivation and possible applications of the problem present in the paper coincide with the small volume problems in hydrodynamics. The differential problem considered in the article is some generalization of the boundary value problem for minimal surface equation.

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