On the stability of explicit finite difference schemes for a pseudoparabolic equation with nonlocal conditions

Jachimavičienė, Justina; Sapagovas, Mifodijus; Štikonas, Artūras; Štikonienė, Olga

doi:10.15388/na.2014.2.6

Cited by 19 publications

(18 citation statements)

References 27 publications

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“…The obtained restriction on discrete step τ and h improves the results of [18], where the conditional stability estimate is proved for τ < h 2 4 (in the case of one-dimensional problem).…”

Section: Explicit Finite Difference Schemessupporting

confidence: 71%

“…In this section we consider the stability of some explicit finite difference schemes, which were proposed and analyzed in [18]. We will generalize these schemes for two-dimensional pseudoparabolic problem and note that three-dimensional problems can be solved in a similar way.…”

Section: Explicit Finite Difference Schemesmentioning

confidence: 99%

“…In [18], one-dimensional version of scheme (6.5) was used in numerical experiments and no stability results are presented. It can be written in the canonical form by taking…”

Section: Explicit Finite Difference Schemesmentioning

confidence: 99%

“…This technique is applied for the stability analysis of parabolic and pseudoparabolic problems with nonlocal boundary conditions in [15,18,19,20]. We note, that in this paper we will not investigate the spectrum of obtained discrete schemes with nonlocal boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The first one is to use explicit finite difference schemes. Here we analyze the stability of explicit algorithms, that are constructed as multidimensional generalizations of one-dimensional algorithms proposed in [18]. Our goal is to apply general results of the stability of three-level finite difference schemes.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On Construction and Analysis of Finite Difference Schemes for Pseudoparabolic Problems With Nonlocal Boundary Conditions

Čiegis

Tumanova

2014

Mathematical Modelling and Analysis

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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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Section: Explicit Finite Difference Schemessupporting

confidence: 71%

Section: Explicit Finite Difference Schemesmentioning

confidence: 99%

“…In [18], one-dimensional version of scheme (6.5) was used in numerical experiments and no stability results are presented. It can be written in the canonical form by taking…”

Section: Explicit Finite Difference Schemesmentioning

confidence: 99%