Yazar "Ashyralyev, Allaberen" seçeneğine göre listele

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    A NOTE ON DIFFERENCE SCHEMES OF NONLOCAL BOUNDARY VALUE PROBLEMS FOR HYPERBOLIC-PARABOLIC EQUATIONS
    (Amer Inst Physics, 2010) Ashyralyev, Allaberen; Özdemir, Yıldırım
    A numerical method is proposed for solving multi-dimensional hyperbolic-parabolic differential equations with the nonlocal boundary condition in t and Dirichlet condition in space variables. The first and second orders of accuracy difference schemes are presented. The stability estimates for the solution and its first- and second-orders difference derivatives are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional hyperbolic-parabolic partial differential equations with variable in x coefficients.
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    A Note on Evolution Equation on Manifold
    (Univ Nis, Fac Sci Math, 2021) Ashyralyev, Allaberen; Sözen, Yaşar; Hezenci, Fatih
    In the present paper, considering the differential equations on smooth closed manifolds, we investigate and establish the well-posedness of boundary value problems nonlocal type for parabolic equations and also hyperbolic equations in Ho center dot lder spaces. Furthermore, in various Ho center dot lder norms we establish new coercivity estimates for the solutions of such type parabolic boundary value problems on manifolds and hyperbolic boundary value problems on manifolds as well.
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    A Note on Hyperbolic Differential Equations on Manifold
    (Amer Inst Physics, 2021) Ashyralyev, Allaberen; Sozen, Yasar; Hezenci, Fatih
    In this extended abstract, considering the differential equations on hyperbolic plane. we investigate and establish the well-posedness of boundary value problem for hyperbolic equations in Holder spaces. Furthermore, we establish new coercivity estimates in various Holder norms for the solutions of such boundary value problems for hyperbolic equations.
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    A Note on Parabolic Difference Equations on Manifold
    (American Institute of Physics Inc., 2022) Ashyralyev, Allaberen; Hezenci, Fatih; Sözen, Y.
    In this work, we consider nonlocal boundary value problems for parabolic equations on manifold. We set up the first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle. For the solutions of the difference scheme, we establish the stability estimates and coercivity estimates in various Hölder norms for the solutions of such boundary value problems. Furthermore, numerical results are given. © 2022 American Institute of Physics Inc.. All rights reserved.
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    A Note on Parabolic Differential Equations on Manifold
    (Amer Inst Physics, 2021) Ashyralyev, Allaberen; Sozen, Yasar; Hezenci, Fatih
    The present extended abstract considers the differential equations on smooth closed manifolds, investigates and establishes the well-posedness of nonlocal boundary value problems (NBVP) in Holder spaces. It also establishes new coercivity estimates in various Holder norms for the solutions of such boundary value problems for parabolic equations.
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    A Note on Stability of Parabolic Difference Equations on Torus
    (Taylor & Francis Inc, 2023) Ashyralyev, Allaberen; Hezenci, Fatih; Sözen, Yaşar
    The present article investigates nonlocal boundary value problems for parabolic equations of reverse type on torus. The first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle T-1 and torus T-2 are presented. For the solutions of the difference scheme, the stability estimates and coercivity estimates in various Holder norms are established. Furthermore, theoretical results are supported by numerical experiments.
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    Numerical approaches for solution of hyperbolic difference equations on circle
    (Walter De Gruyter Gmbh, 2024) Ashyralyev, Allaberen; Hezenci, Fatih; Sozen, Yasar
    The present paper considers nonlocal boundary value problems for hyperbolic equations on the circle T-1 . The first-order modified difference scheme for the numerical solution of nonlocal boundary value problems for hyperbolic equations on a circle is presented. The stability and coercivity estimates in various Holder norms for solutions of the difference schemes are established. Moreover, numerical examples are provided.
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    Numerical solution of a hyperbolic-parabolic problem with nonlocal boundary conditions
    (2012) Ashyralyev, Allaberen; Özdemir, Yıldırım
    A numerical method is proposed for solving hyperbolic-parabolic partial differential equations with nonlocal boundary condition. The first and second orders of accuracy difference schemes are presented. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional hyperbolicparabolic partial differential equations. The method is illustrated by numerical examples.
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    On Numerical Solution of Multipoint NBVP for Hyperbolic-Parabolic Equations with Neumann Condition
    (Amer Inst Physics, 2012) Ashyralyev, Allaberen; Özdemir, Yıldırım
    A numerical method is proposed for solving multi-dimensional hyperbolic-parabolic differential equations with the nonlocal boundary condition in t and Neumann condition in space variables. The first and second orders of accuracy difference schemes are presented. The stability estimates for the solution and its first and second orders difference derivatives are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional hyperbolic-parabolic differential equations with variable in x coefficients.
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    On numerical solutions for hyperbolic-parabolic equations with the multipoint nonlocal boundary condition
    (Pergamon-Elsevier Science Ltd, 2014) Ashyralyev, Allaberen; Özdemir, Yıldırım
    A numerical method is proposed for solving multi-dimensional hyperbolic parabolic differential equations with the nonlocal boundary condition in t and Dirichlet and Neumann conditions in space variables. The first and second order of accuracy difference schemes are presented. The stability estimates for the solution and its first and second orders difference derivatives are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional hyperbolic parabolic differential equations with variable coefficients in x and two-dimensional hyperbolic parabolic equation. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.