A splitting up algorithm for the determination of the control parameter in multi dimensional parabolic problem

Daoud, Daoud S.; Subasi, D. S.

doi:10.1016/j.amc.2004.07.005

Cited by 14 publications

(10 citation statements)

References 9 publications

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“…Therefore, performance of the following algorithm is guaranteed: denominator in right-hand side (19) does not vanish. For negative β, there can be some problems.…”

Section: Numerical Examplesmentioning

confidence: 97%

“…It is important that the sign of function w(x * , t) does not change, i.e. denominator in the right-hand side (19) remain negative.…”

Section: Solution With Alternating Signsmentioning

confidence: 98%

“…. , N − 1 may be represented in the form (16)- (19). Correctness of the computational algorithm follows from fulfilling the condition w n+1 (x * ) = 0.…”

Section: Algorithm For Solving the Inverse Problemmentioning

confidence: 99%

“…The computational algorithm is based on computation of coefficient in new time layer according to (19). This algorithm applicability is ensured under conditions, that denominator does not vanish.…”

Section: Solution With Alternating Signsmentioning

confidence: 99%

“…[13][14][15][16][17] In view of the practical use, we highlight separately the studies dealing with numerical solving inverse problems for multidimensional parabolic equations. [8,18,19] To construct computational algorithms for the identification of the lower coefficient of a parabolic equation, there is widely used idea of transformation of the equation by introducing new unknowns that result in a linear inverse problem. General transformations of some classes of inverse problems for parabolic equations are discussed in the paper [20].…”

Section: Introductionmentioning

confidence: 99%

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Computational algorithms for solving the coefficient inverse problem for parabolic equations

Vabishchevich

Васильев

2014

Inverse Problems in Science and Engineering

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Among inverse problems for partial differential equations, we distinguish coefficient inverse problems, which are associated with the identification of coefficients and/or the right-hand side of an equation using some additional information. When considering time-dependent problems, the identification of the coefficient dependences on space and on time is usually separated into individual problems. In some cases, we have linear inverse problems (e.g. identification problems for the right-hand side of an equation); this situation essentially simplify their study. This work deals with the problem of determining in a multidimensional parabolic equation the lower coefficient that depends on time only. To solve numerically a non-linear inverse problem, linearized approximations in time are constructed using standard finite difference approximations in space. The computational algorithm is based on a special decomposition, where the transition to a new time level is implemented via solving two standard elliptic problems.

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“…Therefore, performance of the following algorithm is guaranteed: denominator in right-hand side (19) does not vanish. For negative β, there can be some problems.…”

Section: Numerical Examplesmentioning

confidence: 97%

“…It is important that the sign of function w(x * , t) does not change, i.e. denominator in the right-hand side (19) remain negative.…”

Section: Solution With Alternating Signsmentioning

confidence: 98%

“…. , N − 1 may be represented in the form (16)- (19). Correctness of the computational algorithm follows from fulfilling the condition w n+1 (x * ) = 0.…”

Section: Algorithm For Solving the Inverse Problemmentioning

confidence: 99%

Section: Solution With Alternating Signsmentioning

confidence: 99%