On the solution of a mathematical model of a viscoelastic bar

  • Arpad Takači
  • Djurdjica Takači
Conference paper

Abstract

A hyperbolic type equation with certain initial and boundary conditions, appropriate for application of the Mikusiński calculus, is considered. Similar problems appeared as mathematical models of the shock between a solid body and a viscoelastic bar.

The exact solution of the corresponding problem in the field of Mikusiński operators is constructed, and the character and regularity of the operational function solution of the problem is analyzed. Then the solution of the starting problem is obtained as a finite sum of continuous functions. An algorithm for constructing an approximate solution is given, and an example is presented.

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References

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    Bergounioux, M., Long, N.T., Dinh, A.P.N.: Mathematical model for a shock problem involving a linear viscoelastic bar. Nonlinear Analysis, Theory, Methods & Applications, 43, 547–561 (2001)MATHCrossRefMathSciNetGoogle Scholar
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    Takači, Dj., Takači, A.: On the approximate solution of mathematical model of a viscoelastic bar. Nonlinear Analysis, Theory, Methods & Applications (in print).Google Scholar
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    Mikusiński, J.: Operational Calculus. Vol.I, PWN — Polish Scientific Publishers, Warszawa and Pergamon Press, Oxford (1983)Google Scholar
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    Long, N.T., Ut, L.V., Truc, N.T.T.: On a shock problem involving a linear viscoelastic bar. Nonlinear Analysis, Theory, Methods & Applications, 63, 198–224 (2005)MATHCrossRefMathSciNetGoogle Scholar
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    Takači, Dj., Takači, A.: The approximate solution of nonlinear equations. Publicationes Mathematicae Debrecen, 65(1–2), 65–79 (2004)MathSciNetGoogle Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Arpad Takači
    • 1
  • Djurdjica Takači
    • 1
  1. 1.Department of Mathematics and Informatics, Faculty of ScienceUniversity of Novi SadNovi SadSerbia

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