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 in | Applied mathematics and computation Vol. 215; no. 7; pp. 2716 - 2732 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Amsterdam
Elsevier Inc
01.12.2009
Elsevier |
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| Online Access | Get full text |
| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/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. |
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| 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. |
| Author_xml | – sequence: 1 givenname: F. surname: Ivanauskas fullname: Ivanauskas, F. organization: Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania – sequence: 2 givenname: T. surname: Meškauskas fullname: Meškauskas, T. email: tadas.meskauskas@mif.vu.lt organization: Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania – sequence: 3 givenname: M. surname: Sapagovas fullname: Sapagovas, M. organization: Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania |
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| Cites_doi | 10.15388/NA.2002.7.1.15204 10.1007/s10625-005-0244-9 10.1016/S0377-0427(99)00200-9 10.1023/B:DIEQ.0000009192.30909.13 10.1023/A:1011961822115 10.15388/NA.2006.11.1.14762 10.1155/S0161171297000215 10.1023/A:1021167932414 10.1016/S0168-9274(01)00139-8 10.1007/BF01931285 10.1007/BF02127706 10.1080/00036819308840181 10.1090/qam/678203 10.1137/0732025 10.1023/A:1021115915575 10.3846/1392-6292.2007.12.131-142 10.1016/j.apnum.2004.02.002 10.1007/s10986-005-0028-1 10.1007/s10625-005-0242-y 10.1080/0020716021000039209 |
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| 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 |
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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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