Single-term Walsh series method for solving Volterra's population model

  • Authors

    • Behnam Sepehrian Arak university
    2014-10-07
    https://doi.org/10.14419/ijamr.v3i4.3431

  • Single-term Walsh series are developed to approximate the solution of the Volterra’s population model. Volterra’s model is a nonlinear integro-di?erential equation where the integral term represents the effect of toxin. Properties of Single-term Walsh series are presented and are utilized to reduce the computation of the Volterra’s population model to some algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples. A comparison is made with existing results.

    Keywords: Volterra’s population model, Numerical methods, STWS method.

  • References

    1. K. Balachandran and K. Murugesan, Analysis of nonlinear singular systems via STWS method, Int. J. Comput. Math. 36(1-2) (1990) 9–12.
    2. K. Balachandran and K. Murugesan, Numerical solution of a singular non-linear system from fluid dynamics, Int. J. Comput. Math. 38(3-4) (1991), 211–218.
    3. C. H. Hsiao and C. F. Chen, Solving integral equations via Walsh functions, Comput. Electr. Engrg. 6 (1979), 279–292.
    4. P. Lancaster, Theory of matrices, Academic Press, New York (1969(.
    5. K. Parand and M. Razzaghi, Rational Chebyshev tau method for solving Volterra's population model, Appl. Math. Comput. 149 (2004) 893–900.
    6. G. P. Rao, K. R. Palanisamy and T. Srinivasan, Extension of computation beyond the limit of initial normal interval in Walsh series analysis of dynamical systems, IEEE Trans. Automat. Control 25(2) (1980) 317–319.
    7. M. Razzaghi and J. Nazarzadeh, Walsh functions, Wiley Encyclopedia of Electrical and Electronics Engineering 23 (1999) 429–440.
    8. P. Sannuti, Analysis and synthesis of dynamic systems via block-pulse functions, Proceedings IEE 124(6) (1977) 571–596.
    9. F. M. Scudo, Volterra and theoritical ecology, Theoret. Popul. Biol. 2 (1971) 1–23.
    10. B. Sepehrian and M. Razzaghi, State analysis of time-varying singular bilinear systems by single-term Walsh series, Int. J. Comput. Math. 80(4) (2003) 413–418.
    11. B. Sepehrian and M. Razzaghi, Solution of time-varying singular nonlinear systems by single-term Walsh series, Math. Prob. Eng. 3 (2003) 129–136.
    12. B. Sepehrian and M. Razzaghi, Solution of nonlinear Volterra-Hammerstein integral equations via single-term Walsh series method, Math. Prob. Eng. 5 (2005) 547–554.
    13. R. D. Small, Population growth in a closed system and mathematical modeling, in: Classroom Notes in Applied Mathematics, SIAM, Philadelphia, PA (1989) 317–320.
    14. K. G. TeBeest, Numerical and analytical solutions of Volterra's population model, SIAM Rev. 39 (1997) 493-484.
    15. A. M. Wazwaz, Analytical approximation and pade approximation for Volterra's population model, Appl. Math. Comput. 100 (1999) 13–25.

  • Downloads

  • How to Cite

    Sepehrian, B. (2014). Single-term Walsh series method for solving Volterra’s population model. International Journal of Applied Mathematical Research, 3(4), 458-463. https://doi.org/10.14419/ijamr.v3i4.3431