Inverse problem for a nonlinear third order in time partial differential equation

Tekin, İbrahim

doi:10.1002/mma.7380

Cited by 5 publications

(4 citation statements)

References 38 publications

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“…Proof of the Theorem 2. Deduction ( 7)-( 31) is also valid in this case since ( 5) is equal to (32). In this case, one needs to develop (33) as follows:…”

Section: A Modification Of (4) With 4th Order Of Convergencementioning

confidence: 99%

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On Various High-Order Newton-Like Power Flow Methods for Well and Ill-Conditioned Cases

2021

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Recently, the high-order Newton-like methods have gained popularity for solving power flow problems due to their simplicity, versatility and, in some cases, efficiency. In this context, recent research studied the applicability of the 4th order Jarrat’s method as applied to power flow calculation (PFC). Despite the 4th order of convergence of this technique, it is not competitive with the conventional solvers due to its very high computational cost. This paper addresses this issue by proposing two efficient modifications of the 4th order Jarrat’s method, which present the fourth and sixth order of convergence. In addition, continuous versions of the new proposals and the 4th order Jarrat’s method extend their applicability to ill-conditioned cases. Extensive results in multiple realistic power networks serve to sow the performance of the developed solvers. Results obtained in both well and ill-conditioned cases are promising.

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“…Proof of the Theorem 2. Deduction ( 7)-( 31) is also valid in this case since ( 5) is equal to (32). In this case, one needs to develop (33) as follows:…”

Section: A Modification Of (4) With 4th Order Of Convergencementioning

confidence: 99%

“…Especially when the coefficients are time-dependent and therefore various systems have to be solved, usually in real-time applications. Clear examples of these kinds of problems are the Moore-Gibson-Thompson equation [32] or the the nonlinear Oskolkov's system [33].…”

Section: Potential Applications Of the Developed Solversmentioning

confidence: 99%

On Various High-Order Newton-Like Power Flow Methods for Well and Ill-Conditioned Cases

2021

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“…The inverse problems of determining time or space dependent coefficients for the higher order in time (more than 2) PDEs attract many scientists. The inverse problem of recovering the solely space dependent and solely time dependent coefficients for the third order in time PDEs are studied by [1] and [21], respectively. More recently, in [9] authors studied the inverse problem of determining time dependent potential and time dependent force terms from the third order in time partial differential equation by considering the critical parameter equal to zero.…”

Section: Introductionmentioning

confidence: 99%

Identification of the time-dependent lowest term in a fourth order in time partial differential equation

Tekin¹

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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“…The inverse problems of determining time or space dependent coefficients for the higher order in time (more than 2) PDEs attract many scientists. The inverse problem of recovering the solely space dependent and solely time dependent coefficients for the third order in time PDEs are studied by [15,16], respectively. More recently, in [17] authors studied the inverse problem of determining time dependent potential and time dependent force terms from the third order in time partial differential equation theoretically and numerically by considering the critical parameter equal to zero.…”

Section: Introductionmentioning

confidence: 99%

Inverse coefficient problem for differential equation in partial derivatives of a fourth order in time with integral over-determination

Huntul¹,

Tekin²

2022

Bul. Kar. Univ. - Math.

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Derivatives in time of higher order (more than two) arise in various fields such as acoustics, medical ultrasound, viscoelasticity and thermoelasticity. The inverse problems for higher order derivatives in time equations connected with recovery of the coefficient are scarce and need additional consideration. In this article the inverse problem of determination is considered which depends on time, lowest term coefficient in differential equation in partial derivatives of fourth order in time with initial and boundary conditions from an additional integral observation is considered. Under some conditions regularity, consistency and orthogonality of data by using of the contraction principle the unique solvability of the solution of the coefficient identification problem on a sufficiently small time interval has been proved.

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Inverse problem for a nonlinear third order in time partial differential equation

Abstract: In this article, we study the inverse problem of recovering a time‐dependent coefficient of a nonlinear third order in time partial differential equation (PDE), which is usually referred to as Moore–Gibson–Thompson equation, from knowledge of a one boundary measurement.

Cited by 5 publications

References 38 publications

On Various High-Order Newton-Like Power Flow Methods for Well and Ill-Conditioned Cases

On Various High-Order Newton-Like Power Flow Methods for Well and Ill-Conditioned Cases

Identification of the time-dependent lowest term in a fourth order in time partial differential equation

Inverse coefficient problem for differential equation in partial derivatives of a fourth order in time with integral over-determination

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