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Numerical stability of DQ solutions of wave problems

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Abstract

In this paper, the solution of one-dimensional (1D) wave problems, by means of the Iterative Differential Quadrature method is discussed in terms of stability and accuracy. The 1D-wave equation with different boundary and initial conditions is considered. The time advancing scheme is here presented in a form, particularly suitable to support the discussion about stability both by the matrix method and by the energy method. The stability analysis, performed by means of these two methods, confirms the conditionally stable nature of the method. The accuracy of the solutions is discussed too.

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References

  1. Zong, Z.: A variable order approach to improve differential quadrature accuracy in dynamic analysis. J. Sound Vib. 266, 307–323 (2003)

    Article  MathSciNet  Google Scholar 

  2. Zong, Z., Lam, K.Y.: A localized differential quadrature (LDQ) method and its application to the 2D wave equation. Comput. Mech. 29, 382–391 (2002)

    Article  MATH  Google Scholar 

  3. Hairer, E., Lubich, C., Cohen, D.: Spectral semi-discretizations of weakly nonlinear wave equations over long times. Isaac Newton Institute Technical Report (2007)

  4. Tomasiello, S.: Stability and accuracy of the iterative differential quadrature method. Int. J. Numer. Methods Eng. 58, 1277–1296 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Tomasiello, S.: A generalization of the IDQ method and a DQ based method to approximate non-smooth solutions. J. Sound Vib. 301, 374–390 (2007)

    Article  MathSciNet  Google Scholar 

  6. Tomasiello, S.: A DQ based approach to simulate the vibrations of buckled beams. Nonlinear Dyn. 50, 37–48 (2007)

    Article  MATH  Google Scholar 

  7. Tomasiello, S.: Numerical solutions of the Burgers-Huxley equation by the IDQ method. Int. J. Comput. Math. 87(1), 129–140 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bellman, R., Casti, J.: Differential quadrature and long-term integration. J. Math. Anal. Appl. 34, 235–238 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bert, C.W., Malik, M.: Differential quadrature method in computational mechanics: a review. Appl. Mech. Rev. 49(1), 1–28 (1996)

    Article  Google Scholar 

  10. Tanaka, M., Chen, W.: Coupling dual reciprocity BEM and differential quadrature method for time-dependent diffusion problems. Appl. Math. Model. 25, 257–268 (2001)

    Article  MATH  Google Scholar 

  11. Szego, G.: Orthogonal Polynomials, vol. 32. AMS Colloquium Publications (1939)

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Authors and Affiliations

  1. DiSGG—Faculty of Engineering, University of Basilicata, C.da Macchia Romana, 85100, Potenza, Italy

    Stefania Tomasiello

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  1. Stefania Tomasiello
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Correspondence to Stefania Tomasiello.

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Tomasiello, S. Numerical stability of DQ solutions of wave problems. Numer Algor 57, 289–312 (2011). https://doi.org/10.1007/s11075-010-9429-2

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  • DOI: https://doi.org/10.1007/s11075-010-9429-2

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