 ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Numerical Solution of Energy Transmission Lines Equivalent Circuit Equations with Adomian Decomposition Method

Journal of Applied Nonlinear Dynamics 5(1) (2016) 65--71 | DOI:10.5890/JAND.2016.03.005

N.F.O. Serteller; D. Ustundag

Marmara University, Electrical-Electronics Engineering, Goztepe, Istanbul

Marmara University, Art and Science Faculty, Mathematics Department, Goztepe, Istanbul

Abstract

In this paper, analysis for a mathematical model of an equivalent circuit to provide solutions of electrical energy power transmission lines (ETL) with Adomian Decomposition Method (ADM) has been proposed. By using Mathematica program, partial differential equations as a function of voltage (current) forming the model are solved and compared with the finite difference method (FDM). The results of some special examples obtained from ADM and FDM illustrate very good synchronism and show the simplicity and the efficiency of the method.

References

1.   Adomian, G. (1998), Solutions of nonlinear PDE, Appl Math Lett, 11, 3, 121-123.
2.   Michalik, M. (2008), Simulation and Analysis of Power System Transients, Lecture Notes.
3.   Lakestani, M. and Saray, B.N., (2010), Numerical Solution of telegraph equation using interpolating scaling functions, Computers and Appplications, 60, 1964-1972.
4.   Srivastava, V.K., Awasthi, M.K., Chaurasia, R.K., and Borenstein, M.T., (2013), The Telegraph Equation and Its Solution by Reduced Differential Transform Method, Hindawi Publishing Corporation Modelling and Simulation in Engineering, 1-7.
5.   Biazar, J. and Ebrahimi, H., (2007), An Approximation to the Solution of Telegraph Equation by Adomian Decomposition Method, International Mathematical Forum, 2 (45), 2231-2236.
6.   Serteller N.F.O. (2011), Electrostatic Analysis of Transmission Lines to Stimulate Corona Discharge at High Voltage, Progress in Electromagnetic research M, 113-117.
7.   Javidi, M. and Nyamoradi, N., (2013), Numerical solution of telegraph equation by using LT inversion Technique, International Journal of Advanced Mathematical Sciences, 1 (2), 64-77.
8.   Delghan, M. and Shokri A. (2007), A Numerical Method for Solving the Hyperbolic Telegraph Equation, Wiley Science, 1080-1095.
9.   Mittal, R. C. and Bhatia, R. (2014), A Collocation Method for Numerical Solution of Hyperbolic Telegraph Equation with Neumann Boundary Condition, Hindawi Publishing, International Computational Mathematics, 2014.