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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 12 | Number 2 | Year 2014 | Article Id. IJMTT-V12P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V12P514

Numerical Investigation of first order linear Singular Systems using Leapfrog Method


S. Sekar, M. Vijayarakavan
Abstract

In this paper numerical investigation of first order linear singular systems of time-invariant and time varying cases [6] using Leapfrog method is considered. The obtained discrete solutions using Leapfrog method are compared with the exact solutions of the first order linear singular systems of time-invariant and time varying cases and single-term Haar wavelet series (STHWS) method. Tables and graphs are presented to show the efficiency of this method. This Leapfrog method can be easily implemented in a digital computer and the solution can be obtained for any length of time.

Keywords
Haar wavelets, Single-term Haar wavelet series, Leapfrog method, Ordinary differential equations, Singular systems.
References

[1] K. Murugesan, Analysis of singular systems using the single-term Walsh series technique, Ph.D. Thesis, Bharathiar University, Coimbatore, Tamil Nadu, India, 1991.
[2] K. Murugesan, D. Paul Dhayabaran and D. J. Evans, “Analysis of different second order systems via Runge-Kutta method”, Intern. J. Comp. Math., vol. 70, pp. 477-493, 1999.
[3] K. Murugesan, D. Paul Dhayabaran and D. J. Evans, “Analysis of different second order multivariable linear system using single term Walsh series technique and Runge- Kutta method”, Intern. J. Comp. Math., vol. 72, pp. 367-374, 1999.
[4] K. Murugesan, D. Paul Dhayabaran, E. C. Henry Amirtharaj and D. J. Evans, “A comparison of extended Runge-Kutta formulae based on variety of means to solve system of IVPs”, Intern. J. Comp. Math., vol. 78, pp. 225-252, 2001.
[5] D. Paul Dhayabaran, A study on second order singular systems using extended RK methods and STWS technique, Ph.D., Thesis, Bharathidasan University, Tiruchirappalli, Tamil Nadu, India, 2000.
[6] S. Sekar, A study on different types of singular systems using RK-Butcher algorithm, Ph.D., Thesis, Bharathidasan University, Tiruchirappalli, Tamil Nadu, India, 2006.
[7] S. Sekar and A. Manonmani, “A study on time-varying singular nonlinear systems via single-term Haar wavelet series”, International Review of Pure and Applied Mathematics, vol.5, pp. 435-441, 2009.
[8] S. Sekar and G.Balaji, “Analysis of the differential equations on the sphere using single-term Haar wavelet series”, International Journal of Computer, Mathematical Sciences and Applications, vol.4, pp.387-393, 2010.
[9] S. Sekar and M. Duraisamy, “A study on CNN based hole-filler template design using single-term Haar wavelet series”, International Journal of Logic Based Intelligent Systems, vol.4, pp.17-26, 2010.
[10] S. Sekar and K. Jaganathan, “Analysis of the singular and stiff delay systems using single-term Haar wavelet series”, International Review of Pure and Applied Mathematics, vol.6, pp. 135-142, 2010.
[11] S. Sekar and R. Kumar, “Numerical investigation of nonlinear volterra-hammerstein integral equations via single-term Haar wavelet series”, International Journal of Current Research, vol.3, pp. 099-103, 2011.
[12] S. Sekar and E. Paramanathan, “A study on periodic and oscillatory problems using single-term Haar wavelet series”, International Journal of Current Research, vol.2, pp. 097-105, 2011.
[13] S. Sekar and M. Vijayarakavan, “Analysis of the non-linear singular systems from fluid dynamics using single-term Haar wavelet series”, International Journal of Computer, Mathematical Sciences and Applications, vol.4, pp. 15-29, 2010.
[14] A. M. Wazwaz, “A comparison of modified Runge-Kutta formula based on a variety of means”, Int. J. Computer Maths, vol. 50, pp. 105-112, 1994.

Citation :

S. Sekar, M. Vijayarakavan, "Numerical Investigation of first order linear Singular Systems using Leapfrog Method," International Journal of Mathematics Trends and Technology (IJMTT), vol. 12, no. 2, pp. 89-93, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V12P514

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