Solving boundary value problems for eigenvalues for linear Hamiltonian systems with a nonlinear dependence on the spectral parameter

 
PIIS003282350002267-3-1
DOI10.31857/S003282350002267-3
Publication type Article
Status Published
Authors
Affiliation: Institute of Problems of Mechanics. A.Yu. Ishlinsky RAS
Address: Russian Federation
Journal namePrikladnaia matematika i mekhanika
EditionVolume 82 Issue 5
Pages605-621
Abstract

  

Keywords
AcknowledgmentThe author thanks LD Akulenko for help in preparing the work. The study was carried out with the financial support of the Russian Foundation for Basic Research (16-31-60078-mol_a_dk).
Received15.12.2018
Publication date18.12.2018
Cite   Download pdf To download PDF you should sign in
Размещенный ниже текст является ознакомительной версией и может не соответствовать печатной

views: 1269

Readers community rating: votes 0

1. Zhuravlev V.F., Klimov D.M. Prikladnye metody v teorii kolebanij. M.: Nauka, 1988. 328 s.

2. Markeev A.P. Linejnye gamil'tonovy sistemy i nekotorye zadachi ob ustojchivosti dvizheniya sputnika otnositel'no tsentra mass. M.; Izhevsk: RKhD, 2009. 396 s.

3. Atkinson F.V. Discrete and Continuous Boundary Problems. N.Y.; L.: Academic Press, 1964. 569 p. = Atkinson F. Diskretnye i nepreryvnye granichnye zadachi. M.: Mir, 1968. 752 s.

4. Reid W.T. Sturmian Theory for Ordinary Differential Equations. N.Y.; B.; Heidelberg: Springer, 1980. 576 p.

5. Arnol'd V.I. Teoremy Shturma i simplekticheskaya geometriya // Funkts. analiz i ego pril. 1985. T. 19. № 4. S. 1–10.

6. Simon Hilscher R. Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems // Math. Nachr. 2014. V. 287 № 5–6. P. 704–716.

7. Sepitka P, Simon Hilscher R. Comparative index and Sturmian theory for linear Hamiltonian systems // J. Diff. Eq. 2017. V. 262. № 2. P. 914–944.

8. Greenberg L., Marletta M. Numerical methods for higher order Sturm–Liouville problems // J. Comput. Appl. Math. 2000. V. 125. № 1–2. P. 367–383.

9. Abramov A.A. Modifikatsiya odnogo metoda resheniya nelinejnoj samosopryazhennoj spektral'noj zadachi dlya gamil'tonovykh sistem obyknovennykh differentsial'nykh uravnenij // ZhVMMF. 2011. T. 51. № 1. S. 39–43.

10. Akulenko L.D., Nesterov S.V. High-Precision Methods in Eigenvalue Problems and Their Applications. Boca Raton, FL, Chapman and Hall/CRC, 2005. 260 p.

11. Akulenko L.D., Nesterov S.V. Opredelenie chastot i form kolebanij neodnorodnykh raspredelennykh sistem s granichnymi usloviyami tret'ego roda // PMM. 1997. T. 61. Vyp. 4. S. 547–555.

12. Akulenko L.D., Gavrikov A.A., Nesterov S.V. Sintez neodnorodnoj uprugoj sistemy s granichnoj nagruzkoj // Vestn. MGU. Ser. 1. Matematika, mekhanika. 2017. Vyp. 5. S. 36–42.

13. Akulenko L.D., Nesterov S.V. Kolebaniya vzaimodejstvuyuschikh sistem s neodnorodnymi raspredelennymi parametrami // Izv. RAN. MTT. 1999. № 2. S. 15–25.

14. Akulenko L.D., Nesterov S.V. Chastotno-parametricheskij analiz sobstvennykh kolebanij neodnorodnykh sterzhnej // PMM. 2003. T. 67. Vyp. 4. S. 588–602.

15. Akulenko L.D., Nesterov S.V. Kolebaniya sterzhnya v neodnorodnoj uprugoj srede // PMM. 2012. T. 76. Vyp. 3. S. 469–475.

16. Akulenko L.D., Gavrikov A.A., Nesterov S.V. Sobstvennye kolebaniya mnogomernykh nelinejnykh po spektral'nomu parametru sistem // DAN. 2017. T. 472. № 6. S. 654–658.

17. Akulenko L.D., Gavrikov A.A., Nesterov S.V. Chislennoe reshenie nelinejnykh po spektral'nomu parametru vektornykh zadach Shturma–Liuvillya s usloviyami Dirikhle // ZhVMMF. 2017. T. 57. № 9. S. 1503–1516.

18. Gavrikov A. Numerical solution of vector Sturm–Liouville problems with a nonlinear dependence on the spectral parameter // AIP Conf. Proc. 2017. V. 1863. № 1. P. 560032.

19. Akulenko L.D., Kalinichenko V.A., Nesterov S.V. Sejshi v kanale s rezkim izmeneniem rel'efa dna // Izv. RAN. MZhG. 2012. № 3. S. 113–121.

20. Sadeghi A., Veisi H., Hassan Saidi M., Asghar Mozafari A. Electroosmotic flow of viscoelastic fluids through a slit microchannel with a step change in wall temperature // J. Heat Transfer. 2013. V. 135. № 2. P. 021706.

21. Akulenko L.D., Nesterov S.V. Vliyanie defekta massy na chastoty i formy prodol'nykh kolebanij sterzhnya // Izv. RAN. MTT. 2014. № 1. S. 135–144.

22. Kalinichenko V.A., Nesterov S.V., So A.N. Volny Faradeya v pryamougol'nom sosude s lokal'nymi neregulyarnostyami dna // Izv. RAN. MZhG. 2015. № 4. S. 83–91.

23. Gavrikov A.A. Numerical solution of eigenproblems for linear Hamiltonian systems and their application to non-uniform rod-like systems // Proc. Int. Conf. DD-2017. 2017. P. 122–128.

24. Akulenko L.D., Gavrikov A.A., Nesterov S.V. Sobstvennye kolebaniya truboprovoda na uprugom osnovanii, transportiruyuschego zhidkost' // Izv. RAN. MTT. 2018. № 1. S. 123–133.

25. Gavrikov A.A. An iterative solution approach to eigenvalue problems for linear Hamiltonian systems and its application to a hybrid system control problem // Proc. IEEE Int. Conf. MMAR 2017. 2017. P. 588–593.

26. Akulenko L.D., Gavrikov A.A. Upravlenie odnomernymi dvizheniyami gibridnykh kolebatel'nykh sistem sterzhnevogo tipa // Izv. RAN. TiSU. 2018. № 3. S. 5–14.

27. Gavrikov A.A., Shamaev A.S. Some problems in acoustics of emulsions // J. Math. Sc. 2011. V. 179. № 3. P. 415–436.

28. Kozlov V.V. Obschaya teoriya vikhrej. Izhevsk: Udmurtskij un-t, 1998. 238 s.

29. Akulenko L.D. Vysokochastotnye sobstvennye kolebaniya mekhanicheskikh sistem // PMM. 2000. T. 64. Vyp. 5. S. 817–832.

30. Vajnberg M.M., Trenogin V.A. Teoriya vetvleniya reshenij nelinejnykh uravnenij. M.: Nauka, 1969. 529 s.

31. Attili B.S., Lesnic D. An efficient method for computing eigenelements of Sturm-Liouville fourth-order boundary value problems // Appl. Math. Comput. 2006. V. 182. P.1247–1254.

32. Syam M.I., Siyyam H.I. An efficient technique for finding the eigenvalues of fourth-order Sturm–Liouville problems // Chaos Solitons Fract. 2009. V. 39. P.659–665.

33. Chanane B. Accurate solutions of fourth order sturm-liouville problems // J. Comput. Appl. Math. 2010. V. 234. P. 3064–3071.

34. Yucel U., Boubaker K. Differential quadrature method (DQM) and Boubaker Polynomials Expansion Scheme (BPES) for efficient computation of the eigenvalues of fourth-order Sturm-Liouville problems // Appl. Math. Modelling. 2012. V. 36. № 1. P. 158–167.

35. Saleh Taher A.H., Maleka A., Momeni-Masuleh S.H. Chebyshev differentiation matrices for efficient computation of the eigenvalues of fourth-order Sturm–Liouville problems // Appl. Math. Modelling. 2012. V. 37. № 7. P. 4634–4642.

36. Greenberg L., Marletta M. Algorithm 775: The code sleuth for solving fourth order sturm-liouville problems // ACM Trans. Math. Software. 1997. V. 23. P. 453–493.

37. Baily P., Everitt W., Zettl A. Computing eigenvalues of singular Sturm–Liouville problems. Results Math. 1991. V.20. P. 391–423.

38. Kollatts L. Zadachi na sobstvennye znacheniya. M: Nauka, 1968. 504 s.

39. Weaver W., Jr., Timoshenko S.P., Young D.H. Vibration Problems in Engineering. N.Y.: Wiley, 1990. 624 p. = Timoshenko S.P., Yang D.Kh., Uiver U. Kolebaniya v inzhenernom dele. 472 s. M: Fizmatlit, 1985.

40. Han S.M., Benaroya H., Wei T. Dynamics of transversely vibrating beams using four engineering theories // J. Sound Vibr. 1999. V. 225. № 5. P. 935–988.

Система Orphus

Loading...
Up