On the Stability of a Weighted Finite Difference Scheme for Hyperbolic Equation with Integral Boundary Conditions

2016 ◽  
pp. 617-626
Author(s):  
Jurij Novickij ◽  
Artūras Štikonas ◽  
Agnė Skučaitė
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Difference Scheme ◽  
Hyperbolic Equation ◽  
Finite Difference Scheme ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
The Stability

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.

The Finite Difference Scheme for 3d Mathematical Modeling of a Wood Drying Process

2001 ◽  
Vol 1 (2) ◽  
pp. 125-137 ◽  
Author(s):  
Raimondas Čiegis ◽  
Vadimas Starikovičius
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Numerical Experiments ◽  
Stability And Convergence ◽  
Finite Difference Schemes ◽  
Drying Process ◽  
The Stability ◽  
Robin Boundary

AbstractThis work discusses issues on the design and analysis of finite difference schemes for 3D modeling the process of moisture motion in the wood. A new finite difference scheme is proposed. The stability and convergence in the maximum norm are proved for Robin boundary conditions. The influence of boundary conditions is investigated, and results of numerical experiments are presented.

scholarly journals ON CONSTRUCTION AND ANALYSIS OF FINITE DIFFERENCE SCHEMES FOR PSEUDOPARABOLIC PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS

2014 ◽  
Vol 19 (2) ◽  
pp. 281-297 ◽  
Author(s):  
Raimondas Čiegis ◽  
Natalija Tumanova
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Two Dimensional ◽  
The Stability

In this paper the one- and two-dimensional pseudoparabolic equations with nonlocal boundary conditions are approximated by the Euler finite difference scheme. In the case of classical boundary conditions the stability of all schemes is investigated by the spectral method. Stability regions of finite difference schemes approximating pseudoparabolic problem are compared with the stability regions of the classical discrete parabolic problem. These results are generalized for problems with nonlocal boundary conditions if a matrix of the finite difference scheme can be diagonalized. For the two-dimensional problem an efficient algorithm is constructed, which is based on the combination of the FFT method and the factorization algorithm. General stability results, known for the three level finite difference schemes, are applied to investigate the stability of some explicit approximations of the two-dimensional pseudoparabolic problem with classical boundary conditions. A connection between the energy method stability conditions and the spectrum Hurwitz stability criterion is shown. The obtained results can be applied for pseudoparabolic problems with nonlocal boundary conditions, if a matrix of the finite difference scheme can be diagonalized.

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