Structural Engineering and Mechanics

  • 제14권3호
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  • Pages.263-285
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  • 2002
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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Numerical solving of initial-value problems by Rbf basis functions

  • 투고 : 2001.02.24
  • 심사 : 2002.07.19
  • 발행 : 2002.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents a numerical procedure for solving initial-value problems using the special functions which belong to a class of Rvachev's basis functions $R_{bf}$ based on algebraic and trigonometric polynomials. Because of infinite derivability of these functions, derivatives of all orders, required by differential equation of the problem and initial conditions, are used directly in the numerical procedure. The accuracy and stability of the proposed numerical procedure are proved on an example of a single degree of freedom system. Critical time step was also determined. An algorithm for solving multiple degree of freedom systems by the collocation method was developed. Numerical results obtained by $R_{bf}$ functions are compared with exact solutions and results obtained by the most commonly used numerical procedures for solving initial-value problems.

키워드

참고문헌

  1. Bathe, K.J. (1982), Finite Element Procedures in Engineering Analysis, Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
  2. Gotovac, B. (1986), "Numerical modelling of engineering problems by smooth finite functions", (in Croatian), Ph.D. Thesis, Faculty of Civil Engineering, University of Zagreb, Zagreb.
  3. Gotovac, B. and Kozuli , V. (1999), "On a selection of basis functions in numerical analyses of engineering problems", Int. J. Engineering Modelling, 12(1-4), 25-41.
  4. Gotovac, B. and Kozuli , V. (2001), "Analyses of thin plate bending by Fup fragment collocation method", Proceedings of the Euroconference on Computational Mechanics and Engineering Practice (COMEP 2001), Szczyrk, Poland, September, 156-161.
  5. Kozuli , V., Gotovac, B. and Damjani , F.B. (1997), "New class of finite functions in the numerical analysis of the process on the continuum", Proc. the 2nd Congress of Croatian Society of Mechanics, Supetar - Croatia, September 1997, 133-140.
  6. Kozuli , V. (1999), "Numerical modeling by the fragment method with $R_{bf}$ functions", (in Croatian), Ph.D. Thesis, Faculty of Civil Engineering, University of Split, Split.
  7. Kozuli , V. and Gotovac, B. (2000), "Numerical analyses of 2D problems using $Fup_n(x,y)$ basis functions", Int. J. Engineering Modelling, 13(1-2), 7-18.
  8. Kozuli , V. and Gotovac, B. (2000), "Hierarchic generation of the solutions of non-linear problems", CD-Rom Proc. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2000), Barcelona, September.
  9. Kravchenko, V.F., Rvachev, V.A. and Rvachev, V.L. (1995), "Mathematical methods for signal processing on the basis of atomic functions", (in Russian), Radiotekhnika i Elektronika, 40(9), 1385-1406.
  10. Kravchenko, V.F., Rvachev, V.A. and Pustovoit, V.I. (1996), "Orthonormalized systems of Wavelet-type based on atomic functions", (in Russian), Doklady Akademii Nauk, 351(1), 16-18
  11. Kravchenko, V.F., Basarab, M.A. and Perez-Meana, H. (2001), "Spectral properties of atomic functions used in digital signal processing", Journal of Communications Technology & Electronics, 46(5), 494-511.
  12. Prenter, P.M. (1989), Splines and Variational Methods, John Wiley & Sons, Inc., New York.
  13. Rvachev, V.L. and Rvachev, V.A. (1971), "On a Finite Function", (in Russian), DAN URSR. Ser. A, 6, 705-707
  14. Rvachev, V.L. and Rvachev, V.A. (1979), Non-classical methods for approximate solution of boundary conditions, (in Russian), Naukova dumka, Kiev.
  15. Timoshenko, S., Young, D.H. and Weaver, W., JR. (1974), Vibration Problems in Engineering, 4th edn, John Wiley & Sons, New York.

피인용 문헌

  1. Adaptive Fup multi-resolution approach to flow and advective transport in highly heterogeneous porous media: Methodology, accuracy and convergence vol.32, pp.6, 2009, https://doi.org/10.1016/j.advwatres.2009.02.013
  2. Maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support vol.228, pp.24, 2009, https://doi.org/10.1016/j.jcp.2009.09.011
  3. Multi-resolution adaptive modeling of groundwater flow and transport problems vol.30, pp.5, 2007, https://doi.org/10.1016/j.advwatres.2006.10.007
  4. Numerical Algorithms for Estimating Probability Density Function Based on the Maximum Entropy Principle and Fup Basis Functions vol.23, pp.12, 2002, https://doi.org/10.3390/e23121559