On self-regularization properties of a difference scheme for linear differential–algebraic equations

In this article a class of linear differential–algebraic equations with an initial condition is identified. This class has a unique continuously differentiable solution that depends on the first derivatives of the right-hand part. Assuming that the right-hand part is given with the known level of th...

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Bibliographic Details
Published in:Applied numerical mathematics 2018-08, Vol.130, p.86-94
Main Authors: Bulatov, Mikhail, Solovarova, Liubov
Format: Article
Language:English
Subjects:
Difference scheme
Differential–algebraic equations
Ill-posed problem
Regularization algorithm
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Summary:In this article a class of linear differential–algebraic equations with an initial condition is identified. This class has a unique continuously differentiable solution that depends on the first derivatives of the right-hand part. Assuming that the right-hand part is given with the known level of the error, it is shown that a difference scheme of the first order generates a regularization algorithm. The integration step that depends on the perturbation of the right-hand part is the regularization parameter. The survey of regularization methods for differential–algebraic equations and related problems is given.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2018.03.015