A note on the parabolic equation with an arbitrary parameter at the derivative

Ashyralyev, Allaberen; Sozen, Yasar

doi:10.1016/j.mcm.2011.06.028

Cited by 4 publications

(4 citation statements)

References 10 publications

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“…Here, v ε (t, s) is the evolution operator (see [16]). This single-step difference scheme (2.1) was previously presented in [15] for the independent in t operator coefficient…”

Section: Uniform Difference Scheme Of Problem (11)mentioning

confidence: 99%

“…Note that generalized stability inequality (2.14) permits us to obtain the estimate of convergence of (2.5) in C τ (E α ). This notation was previously used in [15] for the case of independent in t operator coefficient A(t) = A.…”

Section: Second We Will Define An Operatormentioning

confidence: 99%

“…This notation was previously used in [15] for the case of independent in t operator coefficient A(t) = A. To formulate our result we need to introduce the C β (R n ) , β ∈ [0, 1] of all smooth bounded functions φ(x) defined on R n equipped with the…”

Section: Applicationmentioning

confidence: 99%

“…The role played by uniform difference schemes for partial differential equations with a small parameter in higher order derivatives is well known (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]). …”

Section: Introductionmentioning

confidence: 99%

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On stability of difference schemes in fractional spaces

Ashyralyev

Batyrov²

2013

Mathematical and Computer Modelling

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a b s t r a c tThe Cauchy problem 0)) and with an arbitrary ε positive parameter multiplying the derivative term is considered. The first order of accuracy single-step uniform difference scheme for the solution of this problem is presented. The stability and convergence estimates for the solution of this difference scheme in fractional spaces are obtained. The theorem on the well-posedness of this difference scheme in fractional spaces is established. Convergence estimates for the solution of the Cauchy problem for multi-dimensional parabolic equations with an arbitrary ε positive parameter multiplying the derivative term are obtained.

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“…Here, v ε (t, s) is the evolution operator (see [16]). This single-step difference scheme (2.1) was previously presented in [15] for the independent in t operator coefficient…”

Section: Uniform Difference Scheme Of Problem (11)mentioning

confidence: 99%

Section: Second We Will Define An Operatormentioning

confidence: 99%

Section: Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On stability of difference schemes in fractional spaces

Ashyralyev

Batyrov²

2013

Mathematical and Computer Modelling

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Solution of a singularly perturbed Cauchy problem for linear systems of ordinary differential equations by the method of spectral decomposition

Shaldanbayev¹,

Shomanbayeva²,

Kopzhassarova³

2016

AIP Conference Proceedings

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Asymptotic Solutions of Singular Perturbed Problems with an Instable Spectrum of the Limiting Operator

Kalimbetov

Temirbekov

Khabibullayev

2012

Abstract and Applied Analysis

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The regularization method is applied for the construction of algorithm for an asymptotical solution for linear singular perturbed systems with the irreversible limit operator. The main idea of this method is based on the analysis of dual singular points of investigated equations and passage in the space of the larger dimension, what reduces to study of systems of first-order partial differential equations with incomplete initial data.

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A note on the parabolic equation with an arbitrary parameter at the derivative

Cited by 4 publications

References 10 publications

On stability of difference schemes in fractional spaces

On stability of difference schemes in fractional spaces

Solution of a singularly perturbed Cauchy problem for linear systems of ordinary differential equations by the method of spectral decomposition

Asymptotic Solutions of Singular Perturbed Problems with an Instable Spectrum of the Limiting Operator

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