Application of Sinc-collocation method for solving an inverse problem

Shidfar, A.; Zolfaghari, Reza; Damirchi, J.

doi:10.1016/j.cam.2009.08.003

Cited by 26 publications

(16 citation statements)

References 16 publications

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“…This problem and other similar inverse problems of identifying unknown source parameters have been discussed by several researchers in both one‐ and n ‐dimensional spaces (see, e.g., ). In these problems, the source parameter can be determined with the additional overspecified data.…”

Section: Introductionmentioning

confidence: 95%

Splitting method for an inverse source problem in parabolic differential equations: Error analysis and applications

Shekarpaz

Azari

2019

Numerical Methods Partial

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In this work, we present a numerical method based on a splitting algorithm to find the solution of an inverse source problem with the integral condition. The source term is reconstructed by using the specified data and by employing the Lie splitting method, we decompose the equation into linear and nonlinear parts. Each subproblem is solved by the Fourier transform and then by combining the solutions of subproblems, the solution of the original problem is computed. Moreover, the framework of strongly continuous semigroup (or C0‐semigroup) is employed in error analysis of operator splitting method for the inverse problem. The convergence of the proposed method is also investigated and proved. Finally, some numerical examples in one, two, and three‐dimensional spaces are provided to confirm the efficiency and capability of our work compared with some other well‐known methods.

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Section: Introductionmentioning

confidence: 95%

Splitting method for an inverse source problem in parabolic differential equations: Error analysis and applications

Shekarpaz

Azari

2019

Numerical Methods Partial

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“…The inverse problem (1)-(4) can be used to describe a heat transfer process with a source parameter p(t), where (4) represents the temperature at a given point x * in a spatial domain at time t and u is the temperature distribution. Because of the importance of above problem and other similar inverse problems of identifying unknown source control function, recently much attention has been given in the literature to the development, analysis, and implementation of accurate methods for the numerical solution of them by several authors [6,[8][9][10][11][12][13][14][15][16][17]. In this work, we use the Sinc-collocation method for solving problem (1)-(4) and provide an accurate estimate for the solution u(…”

Section: Introductionmentioning

confidence: 97%

“…Furthermore, the residual error entailed in the Sinc collocation method is known to exhibit an exponential convergence rate [2,4]. These methods have been also employed as forward solvers in the solution of inverse problems [5,6].…”

Section: Introductionmentioning

confidence: 98%

Determination of an unknown function in a parabolic inverse problem by Sinc-collocation method

Shidfar¹,

Zolfaghari²

2010

Numer. Methods Partial Differential Eq.

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In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation is considered. We change the inverse problem to a Volterra integral equation of convolution-type. By using Sinc-collocation method, the resulting integral equation is replaced by a system of linear algebraic equations. The convergence analysis is included, and it is shown that the error in the approximate solution is bounded in the infinity norm by the condition number and the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system. Some examples are given to demonstrate the computational efficiency of the method.

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“…Particular examples include Euler-Bernoulli beam problems [3], elliptic problems [2], Poisson-like problems [28], inverse problem [22], dynamic elasto-plastic problem [1], the generalized regularized long wave(GRLW) equation [19], integral equation [17,18], system of second-order differential equation [7], Sturm-Liouville problems [4], higher-order differential equation [5,21], multiple space dimensions [16], Troesch's problem [6], clamped plate eigenvalue problem [10], biharmonic problems [11], and fourth-order parabolic equation [12].…”

Section: Introductionmentioning

confidence: 99%

Error analysis of sinc-Galerkin method for time-dependent partial differential equations

El-Gamel

2017

Numer Algor

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In this paper, we apply the Galerkin method with sinc bases for solving the boundary-value problems involving nonhomogeneous heat, convection diffusion, wave, and telegraph equations. The accuracy of the method for equation is O(( t) + e −k √ N ). Error analysis is included. Several examples are given to illustrate the efficiency and implementation of the sinc-Galerkin method. Comparisons are made to confirm the reliability of the method.

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Application of Sinc-collocation method for solving an inverse problem

Cited by 26 publications

References 16 publications

Splitting method for an inverse source problem in parabolic differential equations: Error analysis and applications

Splitting method for an inverse source problem in parabolic differential equations: Error analysis and applications

Determination of an unknown function in a parabolic inverse problem by Sinc-collocation method

Error analysis of sinc-Galerkin method for time-dependent partial differential equations

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