On Approximation of Coefficient Inverse Problems for Differential Equations in Functional Spaces

Orlovsky, Dmitry; Piskarev, Sergey

doi:10.1007/s10958-018-3798-9

Cited by 9 publications

(1 citation statement)

References 142 publications

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“…In recent years, many scientists have greatly increased interest in nonclassical boundary value problems (BVPs) for partial differential equations (PDEs) (see and references therein). In particular, methods of solutions source identification problems (SIPs) for PDEs have been extensively studied by several authors in earlier studies, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]22 and bibliography herein).…”

Section: Introductionmentioning

confidence: 99%

On the stable difference scheme for source identification nonlocal elliptic problem

Ashyralyyev

2022

Math Methods in App Sciences

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Approximation of source identification problem for elliptic equation with integral-type nonlocal condition is discussed. The first order of accuracy difference scheme for elliptic nonlocal identification problem is studied. By using spectral resolution of a self-adjoint operator, we establish stability inequalities for solution of constructed scheme. Subsequently, the difference scheme for approximate solution of multidimensional boundary value problem with integral-type nonlocal and first kind boundary conditions is investigated on stability. Numerical test examples are presented.

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Section: Introductionmentioning

confidence: 99%

On the stable difference scheme for source identification nonlocal elliptic problem

Ashyralyyev

2022

Math Methods in App Sciences

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On the second order of accuracy stable difference scheme for integral type non-local elliptic source identification problem

Ashyralyyev¹

2022

Comp. Appl. Math.

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Stable difference schemes for hyperbolic–parabolic equations with unknown parameter

Ashyraliyev,

Ashyralyyeva

2024

Bol. Soc. Mat. Mex.

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In the present paper, we study the first and second order of accuracy difference schemes for the approximate solution of the inverse problem for hyperbolic–parabolic equations with unknown time-independent source term. The unique solvability of constructed difference schemes and the stability estimates for their solutions are obtained. The proofs are based on the spectral representation of the self-adjoint positive definite operator in a Hilbert space.

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On Approximation of Coefficient Inverse Problems for Differential Equations in Functional Spaces

Cited by 9 publications

References 142 publications

On the stable difference scheme for source identification nonlocal elliptic problem

On the stable difference scheme for source identification nonlocal elliptic problem

On the second order of accuracy stable difference scheme for integral type non-local elliptic source identification problem

Stable difference schemes for hyperbolic–parabolic equations with unknown parameter

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