Numerical Solution of linear second order Linear Systems with Singular - A using He’s Variational Iteration Method

S. Sekar; B. Venkatachalam alias Ravikumar

doi:https://doi.org/10.14445/22315373/IJMTT-V36P520

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 36 | Number 2 | Year 2016 | Article Id. IJMTT-V36P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V36P520

Numerical Solution of linear second order Linear Systems with Singular - A using He’s Variational Iteration Method

S. Sekar, B. Venkatachalam alias Ravikumar

Abstract

In this article, He’s Variational Iteration Method (HVIM) is implemented for solving the second order linear systems with singular – A. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of the problem. The results are compared with those obtained by the methods taken from the literature [4]. The works confirms that the He’s Variational Iteration Method is superior and very faster to the other methods.

Keywords

Singular systems, Second order linear systems with singular-A, Leapfrog method, He’s Variational Iteration Method.

References

[1] G. Balaji, S. Vengataasalam and S. Sekar, “Numerical investigation of second order singular system using singleterm Haar wavelet series method”, Journal of Applied Sciences Research, vol. 8, issue 7, pp. 3323-3328, 2012.
[2] J. C. Butcher, “Numerical Methods for Ordinary Differential Equations”, John Wiley & Sons, (2003), New York.
[3] S. L. Campbell, “Singular systems of differential equations II”, Pitman, (1982), London.
[4] S. Karunanithi, S. Chakravarthy and S. Sekar, “Comparison of Leapfrog and single term Haar wavelet series method to solve the second order linear system with singular-A”, Journal of Mathematical and Computational Sciences (JMCS), vol. 4, no. 4, 2014, pp. 804-816.
[5] 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”, International Journal of Computer Mathematics, vol. 72, pp. 367-374, 1999.
[6] S. Sekar and B. Venkatachalam alias Ravikumar, “Numerical solution of linear first order singular systems using He’s Variational Iteration Method”, IOSR Journal of Mathematics, vol. 11, Issue 5, ver. I, pp. 32-36, 2015.
[7] S. Sekar and B. Venkatachalam alias Ravikumar, “Numerical solution of linear second order singular systems He’s Variational Iteration Method”, International Journal of Advanced Science and Engineering Research, vol. 1, Issue 1, pp. 1118-1121, 2016.

Citation :

S. Sekar, B. Venkatachalam alias Ravikumar, "Numerical Solution of linear second order Linear Systems with Singular - A using He’s Variational Iteration Method," International Journal of Mathematics Trends and Technology (IJMTT), vol. 36, no. 2, pp. 134-136, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V36P520