scholarly journals SEMI-IMPLICIT DIFFERENCE SCHEME FOR A TWO-DIMENSIONAL PARABOLIC EQUATION WITH AN INTEGRAL BOUNDARY CONDITION

2017 ◽  
Vol 22 (5) ◽  
pp. 617-633 ◽  
Author(s):  
Kristina Jakubėlienė ◽  
Regimantas Čiupaila ◽  
Mifodijus Sapagovas
Keyword(s):  
Boundary Condition ◽  
Difference Scheme ◽  
Parabolic Equations ◽  
Integral Boundary Conditions ◽  
Two Dimensional ◽  
Implicit Difference Scheme ◽  
Integral Boundary ◽  
Theoretical Investigations ◽  
Regular Splitting ◽  
The Stability

In this paper, we consider a finite difference method for a class of twodimensional parabolic equations with integral boundary conditions. The semi-implicit difference scheme is considered. The stability of difference scheme is proved using the properties of the M-matrices, particularly, the regular splitting of an M-matrix. The numerical results of some examples are presented, that approve our theoretical investigations.

scholarly journals On the stability of a finite difference scheme with two weights for wave equation with nonlocal conditions

2014 ◽  
Vol 55 ◽  
pp. 22-27
Author(s):  
Jurij Novickij ◽  
Artūras Štikonas
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Stability Region ◽  
Nonlocal Conditions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Nonlocal Integral Boundary Conditions ◽  
The Stability ◽  
Param Eters

We consider the stability of a finite difference scheme with two weight param-eters for a hyperbolic equation with nonlocal integral boundary conditions. We obtain stability region in the complex plane by investigating the characteristic equation of a difference scheme using the root criterion. The research was partially supported by the Lithuanian State Science and Studies Foundation, grant MIP-047/2014.

On The Stability Of Finite-Difference Schemes For Parabolic Equations Subject To Integral Conditions With Applications To Thermoelasticity

2008 ◽  
Vol 8 (4) ◽  
pp. 360-373 ◽  
Author(s):  
M SAPAGOVAS ◽  
Z. JESEVICIUTE
Keyword(s):  
Stability Analysis ◽  
Difference Scheme ◽  
Parabolic Equations ◽  
Finite Difference Schemes ◽  
Stability Conditions ◽  
Spectral Structure ◽  
Integral Conditions ◽  
Implicit Difference Scheme ◽  
The Difference ◽  
The Stability

Abstract The stability of implicit difference scheme for parabolic equations subject to integral conditions, which correspond to the quasi-static flexure of a thermoelastic rod is considered. The stability analysis is based on the spectral structure of matrix of the difference scheme. The stability conditions obtained here differ from those presented in the articles of other authors..

scholarly journals Existence and Uniqueness Theorem of Fractional Mixed Volterra-Fredholm Integrodifferential Equation with Integral Boundary Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Shayma Adil Murad ◽  
Hussein Jebrail Zekri ◽  
Samir Hadid
Keyword(s):  
Banach Space ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Existence And Uniqueness Theorem ◽  
Integral Boundary ◽  
Fredholm Type ◽  
Type Integral

We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.

Numerical Simulation of Transient Flow in Products Pipeline

2013 ◽  
Vol 732-733 ◽  
pp. 487-490
Author(s):  
Zhen Ye Wang ◽  
Jiang Fei Li ◽  
Lian Yuan ◽  
Zhi Zhong Fu ◽  
Bo Li ◽  
...  
Keyword(s):  
Difference Scheme ◽  
Large Time ◽  
Transient Flow ◽  
Implicit Difference Scheme ◽  
Time Step ◽  
Characteristics Method ◽  
Large Time Step ◽  
The Stability ◽  
Products Pipeline ◽  
Stability And Accuracy

In this paper, explicit difference scheme, implicit difference scheme and characteristics method are separately used to simulate the transient flow in products pipeline. The simulation result can be used to prevent water hammer in the pipeline of unsteady situation and to improve the efficiency and safety in oil transmission systems. And then, the stability and accuracy of the three methods are compared by adopting different time steps. For explicit difference method, large fluctuation may occur in case of large time step. For implicit method, the result is weakly affected by time step, only if the relaxation factor selected is reasonable. For characteristics method, the results have a high convergence speed and precision. The results show that, in the situation of valve shut down in terminal, it takes about 1.1×104 seconds to return to a new steady state.

scholarly journals On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic-Parabolic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Allaberen Ashyralyev ◽  
Okan Gercek
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Approximate Solutions ◽  
Second Order ◽  
Well Posedness ◽  
Parabolic Differential Equations ◽  
Implicit Difference Scheme ◽  
Order Of Accuracy

We are interested in studying a second order of accuracy implicit difference scheme for the solution of the elliptic-parabolic equation with the nonlocal boundary condition. Well-posedness of this difference scheme is established. In an application, coercivity estimates in Hölder norms for approximate solutions of multipoint nonlocal boundary value problems for elliptic-parabolic differential equations are obtained.

scholarly journals Robustness of Polynomial Stability of Damped Wave Equations

2022 ◽  
Author(s):  
Dmytro Baidiuk ◽  
Lassi Paunonen
Keyword(s):  
Boundary Condition ◽  
Wave Equations ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Polynomial Stability ◽  
One Dimensional ◽  
Acoustic Boundary Condition ◽  
The Stability ◽  
Perturbed Equation ◽  
Dimensional Wave

AbstractIn this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional wave equations on rectangular domains, a one-dimensional weakly damped Webster’s equation, and a wave equation with an acoustic boundary condition. In the case of Webster’s equation, we use our results to compute explicit numerical bounds that guarantee the polynomial stability of the perturbed equation.

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