Strongly damped stiff oscillator under external force: a case study

Computer Science & Engineering

Authors

First and Last Name Academic degree E-mail Affiliation
Winfried Auzinger Ph.D. w.auzinger [at] tuwien.ac.at TU Wien, Austria, Institute of Analysis and Scientific Computing
Vienna, Austria

I and my co-authors (if any) authorize the use of the Paper in accordance with the Creative Commons CC BY license

First published on this website: 03.09.2019 - 20:19
Abstract

This is a numerical study of ODE systems modelling the dynamics of a strongly damped stiff oscillator under periodic force. After reviewing the notion of stiffness, we demonstrate and discuss convergence order reduction for some well-established numerical integrators. We also include some comments on stiffness in nonlinear systems.
 

References

[1] Auzinger, W. (2016). A note on similarity to contraction for stable 2 x 2 companion matrices.  Ukr. Math. J., 68(3), 448-457.
[2] Auzinger, W.,  Frank, R., Kirlinger, G. (1990). A note on convergence concepts for stiff problems. Computing 44, 197-208.
[3] Auzinger, W., Stolyarchuk, R. (2016). A topic in the stability analysis associated with companion matrices. Matematychni Studii 46(2), 115-120.
[4] Dahlquist, G. (1963). A special stability problem for linear multistep methods.  BIT 3(1), 27-43.
[5] Hairer, E., Wanner, G. (1996). Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems (2nd ed.). Springer-Verlag, Berlin, Heidelberg, New York.
[6] Hochbruck, M., Ostermann, A. (2019). Exponential integrators.  Acta Numerica 19, 209­286.
[7] Prothero A., Robinson, A. (1974).  On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations. Math. Comp. 28, 145-162.
[8] Trefethen, L.N., Embree M. (2005). Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princetown University Press.
[9] Auzinger, W., Frank, R., Stetter, H.J. (1996). Vienna contributions to the development of RK-methods.  Appl. Numer. Math. 22, 35-49.
[10] www.maplesoft.com

Full text

Comments

auzinger
researcher

x

Tue, 09/03/2019 - 20:35
auzinger
researcher

4.9.2019: new version uploaded (typing error corrected)

Wed, 09/04/2019 - 08:37
Secretary CSE
researcher, secretary

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:

  • International participants – 100 EUR;
  • Participants from Ukraine – 450 UAH.

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

 

Thu, 10/17/2019 - 13:28