Numerical solution of the nonlinear evolutional inverse problem related to elastoplastic torsional problem

Tatar, Salih; Muradoğlu, Zahir

doi:10.1080/00036811.2013.823479

Cited by 6 publications

(4 citation statements)

References 25 publications

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“…The direct problem (8) and the inverse problem (9) have been well-studied both theoretically and numerically in the mathematical literature [36].…”

Section: Introductionmentioning

confidence: 99%

Analysis of direct and inverse problems for a fractional elastoplasticity model

Tatar¹,

Ulusoy

2017

Filomat

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This study is devoted to a nonlinear time fractional inverse coeficient problem. The unknown coefficient depends on the gradient of the solution and belongs to a set of admissible coefficients. First we prove that the direct problem has a unique solution. Afterwards we show the continuous dependence of the solution of the corresponding direct problem on the coefficient, the existence of a quasi-solution of the inverse problem is obtained in the appropriate class of admissible coefficients.

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“…The direct problem (8) and the inverse problem (9) have been well-studied both theoretically and numerically in the mathematical literature [36].…”

Section: Introductionmentioning

confidence: 99%

Analysis of direct and inverse problems for a fractional elastoplasticity model

Tatar¹,

Ulusoy

2017

Filomat

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“…Inverse problems have a practical importance among the pressing problems of current mathematical research. The determination of unknown coefficients in nonlinear partial differential equations of different types from additional conditions that is boundary or surface measured data are well known in the literature as inverse coefficient problems ( [2][3][4][5][6] and references therein). Hasanov and Liu studied an inverse problem associated with a nonlinear parabolic initial value problem [7] with an unknown leading coefficient : = (|∇ | 2 )of the equation − ∇( (|∇ | 2 )∇ ) + ( , ) = ( , ).…”

Section: Introductionmentioning

confidence: 99%

Determination of Young's modulus by using initial data for different boundary conditions

Ilhan¹,

Muradoğlu²

2017

ams

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It is well known that modulus of elasticity, i.e. Young's modulus measures stiffness of an elastic material. This paper proposes a rapid inverse analysis approach based on a measured deflection at some interior point on the middle surface of an elastic plate. An algorithm is developed to identify an unknown modulus of elasticity for a given maximal deflection and the corresponding force. Computational results with noise free and noisy data show effectiveness of the proposed approach.

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“…This inverse problem as well as some other similar inverse parabolic problems has recently attracted much attention, and various numerical methods are developed for these problems (see for example, [1,[8][9][10][11][12]14,15,20,22,23,29,30,[32][33][34][35][36][37][38]). …”

Section: Introductionmentioning

confidence: 99%

“…(5) represents the temperature at a given point x * , in a spatial domain at time t . Thus, the purpose of solving this inverse problem is to identify the source parameter that will produce at each time t a desired temperature at a given point x * in a spatial domain [2,15,22,35,37].…”

Section: Introductionmentioning

confidence: 99%

Cardinal Hermite interpolant multiscaling functions for solving a parabolic inverse problem

Ashpazzadeh¹,

Lakestani²,

Razzaghi³

2017

Turk J Math

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An effective method based upon cardinal Hermite interpolant multiscaling functions is proposed for the solution of the one-dimensional parabolic partial differential equation with given initial condition and known boundary conditions and subject to overspecification at a point in the spatial domain. The properties of multiscaling functions are first presented. These properties together with a collocation method are then utilized to reduce the parabolic inverse problem to the solution of algebraic equations. The scheme described is efficient. The numerical results obtained using the present algorithms for test problems show that this method can solve the model effectively.

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Numerical solution of the nonlinear evolutional inverse problem related to elastoplastic torsional problem

Cited by 6 publications

References 25 publications

Analysis of direct and inverse problems for a fractional elastoplasticity model

Analysis of direct and inverse problems for a fractional elastoplasticity model

Determination of Young's modulus by using initial data for different boundary conditions

Cardinal Hermite interpolant multiscaling functions for solving a parabolic inverse problem

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