Fitted Difference Schemes for Delay Convection-Diffusion Problems with Small Parameter
Newer version | Date Published | |
---|---|---|
New version of a paper 2 | 02.11.2019 - 01:22 |
Discussion is closed on this version, please comment on the latest version above |
New version of a paper 1 | 02.11.2019 - 01:23 |
Discussion is closed on this version, please comment on the latest version above |
I and my co-authors (if any) authorize the use of the Paper in accordance with the Creative Commons CC BY license
This study deals with initial value problem for linear second-order delay differential equation with small parameter. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first order uniform convergence in the discrete maximum norm. The difference scheme isshown to be uniformly convergent to the continuous solution with respect tothe perturbation parameter. A numerical example is solved using the presented method and compared the computed result with exact solution of the problem.
[1] R. Bellman, K.L. Cooke, Differential-Difference Equations,
Academy Press, New York, 1963.
[2] R.D. Driver, Ordinary and Delay Differential Equations,
Belin-Heidelberg, New York, Springer, 1977.
[3] A. Bellen, M. Zennaro, Numerical methods for delay differential
equations, Oxford University Press, Oxford, (2003).
[4] B.J.MacCartin, Exponential fitting of the delayed recruitment/renewal equation. J. Comput. Appl. Math., 136(2001)343-356.
[5] M. W. Derstine, F. A. H. H. M. Gibbs, and D. L. Kaplan, Bifurcation gap in a hybrid optical system, Phys. Rev. A, 26 (1982)3720-3722.
[6] A. Longtin, J. Milton, Complex oscillations in the human pupil
light reflex with mixed and delayed feedback, Math. Biosci. 90 (1988)183-199.
[7] M.C. Mackey, L. Glass, Oscillation and chaos in physiological
control systems, Science, 197(1977)287-289.
[8] E. R. Doolan, J.J.H. Miller, and W. H. A. Schilders, Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole, Press, Dublin, 1980.
[9] P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E.O'Riordan and G.I.Shishkin, Robust Computational Techniques for Boundary Layers
Chapman-Hall/CRC, New York, 2000.
[10] H.G. Roos, M. Stynes and L. Tobiska, Numerical Methods for Singularly Perturbed Differential Equations, Convection-Diffusion and Flow Problems, Springer Verlag, Berlin, 1996.
[11] G. M. Amiraliyev, and Y.D.Mamedov, Difference schemes on the
uniform mesh for singularly perturbed pseudo-parabolic equations, Tr. J. of
Math.,19(1995) 207-222.
[12] G.M. Amiraliyev and H. Duru, A uniformly convergent finite difference method for a initial value problem, Applied Mathematics and Mechanics, 20,4(1999) 363-370.
[13] G.M. Amiraliyev, F. Erdogan, Uniform numerical method for
singularly perturbed delay differential equations, J.Comput. Math.
Appl. 53(2007)1251-1259.
[14] H. Tian, The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag, J.
Math. Anal. Appl. 270(2002)143-149.
[15] S. Maset, Numerical solution of retarded functional differential equations as abstract Cauchy problems, J. Comput. Appl. Math. 161, 259-282, (2003).
[16] J.Mallet-Paret, R.D. Nussbaum, A differential-delay equations arising in optics and physicology, SIAM J. Math. Anal. 20,
249-292, (1989).
[17] C.G. Lange,R.M. Miura, Singular perturbation analysis of boundary-value problems for differential-difference equations. v. small shifts with layer behavior, SIAM J. Appl. Math. 54 (1994) 249-272.
[18] C.G. Lange, R.M. Miura, Singular perturbation analysis of boundary-value problems for differential difference equations,
SIAM J. Appl. Math. 42, 502-531, (1982).
[19] M.K. Kadalbajoo, K.K. Sharma, Numerical analysis of boundary-value problems for singularly-perturbed differential-difference equations with small shifts of mixed type.
Journal of Optimization Theory and Applications.115 (2002) 145-163.
Comments
Dear Authors,
Your paper has been accepted!
We are glad to inform you that your conference paper has been accepted to participate in the 9th International Youth Science Forum «Litteris et Artibus» (November 21-23, 2019, Lviv, Ukraine)! Your paper will be published in digital proceedings with ISSN and DOI on the website https://openreviewhub.org/lea
Please, answer the following participation questions:
• Are you going to take part in the conference in person?
• Do you require official invitation letter from Lviv Polytechnic? (The invitation letter will be scanned and sent to your e-mail).
Presentation delivery regulations:
Conference participants will present their work on posters. Content and design of posters is arbitrary, but it should include the basic provisions of your paper: author names, title, main points, equations, figures etc. as well as exclude solid color, gradient or other costly to print backgrounds. The poster's upper part may include some information about your organization (title and logo, brief contact information).
Selected papers will be presented orally.
We also ask you to cover the conference fee till October 25, 2019:
Conference fees include online paper publication and organizational expenses. Cost of accommodation, meals and social program are not included.
Please note, that invitation will be sent and proceedings will be implemented only after 100% payment fee.
If you need help with accommodation, please send a request to the Secretary. Invitations to lunch will be available for purchase at the registration desk.
The conference fee’s payment details:
Account details for payment of the participation fee from Ukraine participants (in UAH):
Одержувач: Первинна профспілкова організація студентів та аспірантів Національного університету «Львівська політехніка»
Банк: Акціонерний банк «Південний»
Код установи банку: 20953647
МФО: 328209
код за ЄДРПОУ (ІПН): 20846213
Номер рахунку: 26004010050168
Призначення платежу: П.І.Б, оргвнесок за участь у конференції «LEA-2019»
Account details for payment of the participation fee by international participants (in EURO):
Beneficiary: Lviv Polytechnic Alumni Association
IBAN: UA753805820000026002010325122
Bank of Beneficiary: INTERNATIONAL INVESTMENT BANK
Bank Address: 16, LAVRSKA STR., KYIV, UKRAINE
SWIFT code: IINBUAUK
Corraccount No.: 400 8866 75800
With Correspondent Bank: COMMERZBANK AG, Frankfurt am Main, Germany
SWIFT code: COBADEFF
The full Forum’s program will be published on the https://openreviewhub.org/lea before November 1, 2019.
Looking forward to receiving your poster! See you in Lviv soon!
Best regards,
Natallia Veretennikova,
The CSE Secretary
The newest version of my paper is attached
The newest version of my paper is attached