A Numerical Solution to a Problem of Crystal Energy Spectrum Determination by the Heat Capacity  Dependent on a Temperature

Tanana, V.P.; Sidikova, A. I.; Ershova, A.A.

doi:10.32523/2306-6172-2017-5-1-87-94

Cited by 2 publications

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“…Then, by implementing the discretization process, we obtain the linear operator equation. The inverse ill-posed problems have been studied and solved in many works with a different method [11][12][13][14].…”

Section: Problem Statementmentioning

confidence: 99%

“…[8] and many others. Various methods and algorithms for solving IP "inverse problems" were explained and used in [9][10][11][12][13][14][15][16][17][18][19]. The success of these methods and algorithms is largely based on understanding and analyzing the mathematical problems related to the declarations of the properties in these IP "inverse problems" and identifying specific difficulties in solving them [20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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Multigrid Method for Solving Inverse Problems for Heat Equation

et al. 2022

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In this paper, the inverse problems for the boundary value and initial value in a heat equation are posed and solved. It is well known that those problems are ill posed. The problems are reformulated as integral equations of the first kind by using the separation-of-variables method. The discretization of the integral equation allowed us to reduce the integral equation to a system of linear algebraic equations or a linear operator equation of the first kind on Hilbert spaces. The Landweber-type iterative method was used in order to find an approximation solution. The V-cycle multigrid method is used to obtain more frequent and fast convergence for iteration. The numerical computation examples are presented to verify the accuracy and fast computing of the approximation solution.

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Section: Problem Statementmentioning

confidence: 99%