Numerical Solution of the Non-Linear Singular Systems from Fluid Dynamics Using Leapfrog Method

  • Authors

    • M. Vijayarakavan
    • V. Amirthalingam
    https://doi.org/10.14419/ijet.v7i3.10.25311

    Received date: January 3, 2019

    Accepted date: January 3, 2019

    Published date: April 28, 2026

  • Fluid Dynamics, Single-Term Haar Wavelet Series, Singular Non-Linear Systems.

  • Abstract

    In this Research article, the new proposed technique for examination of the singular non-linear problem from Fluid dynamics utilizing Leapfrog Method is exhibited. To represent the adequacy of the Leapfrog Method, the different cases in singular non-linear system from Fluid dynamics have been considered and contrasted and the Single Term Haar Wavelet Series and results are observed to be extremely precise. The arrangements of the non-singular particular problems from Fluid dynamics are introduced in the tables. The proposed method can be effortlessly utilized in an advanced Computer.

  • References

    1. J. C. Butcher, “The numerical analysis of ordinary differential equations Runge Kutta and general linear methods”, John Wiley and Sons, New York, (1987).
    2. J. C. Butcher, Numerical Methods for Ordinary Differential Equa-tions, John Wiley & Sons, New York, (2003).
    3. K. Murugesan, “Analysis of singular systems using the single-term Walsh series technique”, Ph.D. Thesis, Bharathiar University, Coimbatore, Tamil Nadu, India, 1991.
    4. K. Murugesan, D. Paul Dhayabaran and D. J. Evans, “Analysis of Non-Linear singular system from Fluid dynamics using extended Runge-Kutta methods”, Intern. J. Comp. Math., 76, (2000), 239-266.
    5. 14 S. L. Campbell, “Bilinear nonlinear descriptor control systems”, CRSC Tech. Rept. 102386-01, Department of Mathematics, N. C. State University, Raleigh, (1987) NC 27695.
    6. 15 S. L. Campbell and J. Rodriguez, “Non-linear singular sys-tems and contraction mappings”, Proceedings of the Amer-ican Control Conference, (1984), 1513-1519.
    7. 16 S. L. Campbell, “One canonical form for higher index linear time-varying singular systems, Circuits, Systems and Signal Pro-cessing”, 2, (1983), 311-326.
    8. N. Wiener, Cybermetics, MIT Press, Cambridge, (1948).
    9. F. L. Lewis, B. C. Mertzios and W. Marszalek, “Analysis of singu-lar bilinear systems using Walsh functions”, IEE Proc. Pt. D., 138, (1991), 89-92.
    10. F. L. Lewis, B. C. Mertzios, G. Vachtseyanos and M. A. Chris-todoulou, “Analysis of bilinear systems using Walsh functions”, IEEE Trans. Automat. Contr., 35, (1990), 119-123.
    11. K. Balachandran and K. Murugesan, “Numerical solution of singu-lar non-linear system from Fuid dynamics”, Intern. J. Comp. Math., 38, (1991), 211-218.
    12. K. Murugesan, D. Paul Dhayabaran and D. J. Evans, “Analysis of Non-Linear singular system from Fluid dynamics us-ing extended Runge-Kutta methods”, Intern. J. Comp. Math., 76, (2000), 239-266.
    13. S. Sekar and M. Vijayarakavan, “Analysis of the non-linear singular systems from Fuid dynamics using single-term Haar wave-let series", International Journal of Computer, Mathematical Scienc-es and Applications, vol. 4, nos. 1-2, 2010, pp. 15-29.
    14. Murugesan, K., Paul Dhayabaran, D. and Evans, D. J. (2000) “Analysis of Non-linear Singular System from Fluid Dynamics us-ing Extended Runge-Kutta Methods”, International Journal of Computer Mathematics, 76, pp. 239-266.
    15. D. J. Evans, K. Murugesan, S. Sekar and Hyun-Min Kim, “Non-linear singular system using RK-Butcher Algorithms”, Inter-national Journal of Computer Mathematics, Vol.83, No.1, 2006, pp. 131-142.

  • Downloads

  • How to Cite

    Vijayarakavan, M., & Amirthalingam, V. (2026). Numerical Solution of the Non-Linear Singular Systems from Fluid Dynamics Using Leapfrog Method. International Journal of Engineering and Technology, 7(3.10), 97-100. https://doi.org/10.14419/ijet.v7i3.10.25311