Asymptotic Estimates of the Solution of a Restoration Problem with an Initial Jump

Author

Nurgabyl, Duisebek

Source

Journal of Applied Mathematics

Issue

Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-11, 11 p.

Publisher

Hindawi Publishing Corporation

Publication Date

2014-04-24

Country of Publication

Egypt

No. of Pages

11

Main Subjects

Mathematics

Abstract EN

The asymptotic behavior of the solution of the singularly perturbed boundary value problem Lεy=htλ,Liy+σiλ=ai,i=1,n+1̅ is examined.

The derivations prove that a unique pair (ỹt,λ̃ε,ε,λ̃ε) exists, in which components y(t,λ̃ε,ε) and λ̃(ε) satisfy the equation Lεy=h(t)λ and boundary value conditions Liy+σiλ=ai,i=1,n+1̅.

The issues of limit transfer of the perturbed problem solution to the unperturbed problem solution as a small parameter approaches zero and the existence of the initial jump phenomenon are studied.

This research is conducted in two stages.

In the first stage, the Cauchy function and boundary functions are introduced.

Then, on the basis of the introduced Cauchy function and boundary functions, the solution of the restoration problem Lεy=htλ,Liy+σiλ=ai,i=1,n+1̅ is obtained from the position of the singularly perturbed problem with the initial jump.

Through this process, the formula of the initial jump and the asymptotic estimates of the solution of the considered boundary value problem are identified.

American Psychological Association (APA)

Nurgabyl, Duisebek. 2014. Asymptotic Estimates of the Solution of a Restoration Problem with an Initial Jump. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-511239

Modern Language Association (MLA)

Nurgabyl, Duisebek. Asymptotic Estimates of the Solution of a Restoration Problem with an Initial Jump. Journal of Applied Mathematics No. 2014 (2014), pp.1-11.
https://search.emarefa.net/detail/BIM-511239

American Medical Association (AMA)

Nurgabyl, Duisebek. Asymptotic Estimates of the Solution of a Restoration Problem with an Initial Jump. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-511239

Data Type

Journal Articles

Language

English

Notes

Includes bibliographical references

Record ID

BIM-511239