Stability of difference schemes for two-dimensional parabolic equations with non-local boundary conditions

The stability of difference schemes for one-dimensional and two-dimensional parabolic equations, subject to non-local (Bitsadze–Samarskii type) boundary conditions is dealt with. To analyze the stability of difference schemes, the structure of the spectrum of the matrix that defines the linear syste...

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Published inApplied mathematics and computation Vol. 215; no. 7; pp. 2716 - 2732
Main Authors Ivanauskas, F., Meškauskas, T., Sapagovas, M.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.12.2009
Elsevier
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ISSN0096-3003
1873-5649
DOI10.1016/j.amc.2009.09.012

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Abstract The stability of difference schemes for one-dimensional and two-dimensional parabolic equations, subject to non-local (Bitsadze–Samarskii type) boundary conditions is dealt with. To analyze the stability of difference schemes, the structure of the spectrum of the matrix that defines the linear system of difference equations for a respective stationary problem is studied. Depending on the values of parameters in non-local conditions, this matrix can have one zero, one negative or complex eigenvalues. The stepwise stability is proved and the domain of stability of difference schemes is found.
AbstractList The stability of difference schemes for one-dimensional and two-dimensional parabolic equations, subject to non-local (Bitsadze–Samarskii type) boundary conditions is dealt with. To analyze the stability of difference schemes, the structure of the spectrum of the matrix that defines the linear system of difference equations for a respective stationary problem is studied. Depending on the values of parameters in non-local conditions, this matrix can have one zero, one negative or complex eigenvalues. The stepwise stability is proved and the domain of stability of difference schemes is found.
Author Meškauskas, T.
Sapagovas, M.
Ivanauskas, F.
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  surname: Sapagovas
  fullname: Sapagovas, M.
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Issue 7
Keywords Non-local boundary conditions
Parabolic equations
Finite difference schemes
Stepwise stability
Transcendental equation
Difference scheme
Eigenvector
Numerical linear algebra
Eigenvalue
Iterative method
Boundary condition
Equation system
Non linear equation
Direct method
Two dimensional equation
Parabolic equation
Numerical analysis
Linear system
Linear equation
Matrix inversion
Applied mathematics
Algebraic equation
Numerical stability
Finite difference method
Language English
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Snippet The stability of difference schemes for one-dimensional and two-dimensional parabolic equations, subject to non-local (Bitsadze–Samarskii type) boundary...
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SubjectTerms Algebra
Algebraic geometry
Exact sciences and technology
Finite difference schemes
Mathematical analysis
Mathematics
Non-local boundary conditions
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Operator theory
Parabolic equations
Sciences and techniques of general use
Stepwise stability
Title Stability of difference schemes for two-dimensional parabolic equations with non-local boundary conditions
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