On the Structure of the Spectrum of a Differential Operator with a Nonlocal Condition

Sapagovas, Mifodijus; Štikonas, Artūras

doi:10.1007/s10625-005-0242-y

Cited by 53 publications

(67 citation statements)

References 9 publications

(17 reference statements)

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“…The eigenvalues of problem (4.1)-(4.2) depend on the parameters γ and ξ. Regarding to the results presented in the paper [25] we conclude the following:…”

Section: Nonlocal Bitsadze -Samarskii Conditionmentioning

confidence: 51%

On Stability Analysis of Finite Difference Schemes for Generalized Kuramoto-Tsuzuki Equation With Nonlocal Boundary Conditions

Leonavičienė

Bugajev

Jankevičiūtė

et al. 2016

Mathematical Modelling and Analysis

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Abstract. A general methodology for the stability analysis of discrete approximations of nonstationary PDEs is applied to solve the Kuramoto-Tsuzuki equation, including also the Schrödinger problem. Stability regions are constructed for the explicit, backward and symmetrical Euler schemes. The obtained results are applied to solve the Kuramoto-Tsuzuki problem with a non-local integral boundary condition. Results of computational experiments are provided.

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“…The eigenvalues of problem (4.1)-(4.2) depend on the parameters γ and ξ. Regarding to the results presented in the paper [25] we conclude the following:…”

Section: Nonlocal Bitsadze -Samarskii Conditionmentioning

confidence: 51%

On Stability Analysis of Finite Difference Schemes for Generalized Kuramoto-Tsuzuki Equation With Nonlocal Boundary Conditions

Leonavičienė

Bugajev

Jankevičiūtė

et al. 2016

Mathematical Modelling and Analysis

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“…The idea to reduce the system of difference equations with nonlocal conditions to the two systems of the same type with the Dirichlet conditions was also used earlier for the solution of the elliptic equations with the nonlocal conditions of the special type [27,28]. But in all quoted papers, the iterative methods for solutions of the systems of difference equations with nonlocal conditions were not considered.…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

“…was investigated in article [28]. There were noticed that the matrix of the difference equation can have zero, negative, complex or multiple eigenvalues depending on the values of γ and ξ.…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

On iterative methods for some elliptic equations with nonlocal conditions

Štikonienė

Sapagovas

Čiupaila

2014

NAMC

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Abstract. The iterative methods for the solution of the system of the difference equations derived from the elliptic equation with nonlocal conditions are considered. The case of the matrix of the difference equations system being the M-matrix is investigated. Main results for the convergence of the iterative methods are obtained considering the structure of the spectrum of the difference operators with nonlocal conditions. Furthermore, the case when the matrix of the system of difference equations has only positive eigenvalues was investigated. The survey of results on convergence of iterative methods for difference problem with nonlocal condition is also presented.

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“…The spectrum and characteristic functions for eigenvalues of Sturm-Liouville problem are widely investigated in [9][10][11][12]. For example, the following problemś…”

Section: Introductionmentioning

confidence: 99%

On the stability of a weighted finite difference scheme for wave equation with nonlocal boundary conditions

Novickij

Štikonas

2014

NAMC

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On the Structure of the Spectrum of a Differential Operator with a Nonlocal Condition

Cited by 53 publications

References 9 publications

On Stability Analysis of Finite Difference Schemes for Generalized Kuramoto-Tsuzuki Equation With Nonlocal Boundary Conditions

On Stability Analysis of Finite Difference Schemes for Generalized Kuramoto-Tsuzuki Equation With Nonlocal Boundary Conditions

On iterative methods for some elliptic equations with nonlocal conditions

On the stability of a weighted finite difference scheme for wave equation with nonlocal boundary conditions

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