• editor.aipublications@gmail.com
  • Track Your Paper
  • Contact Us
  • ISSN: 2456-866X

International Journal Of Chemistry, Mathematics And Physics(IJCMP)

Exact Solutions of Coupled Parallel Resonant Circuits Equations by Decomposition Method

E. U. Agom , F. O. Ogunfiditimi , I. M. Esuabana , B. E. A. Eno


International Journal of Chemistry, Mathematics And Physics(IJCMP), Vol-2,Issue-2, March - April 2018, Pages 19-22 , 10.22161/ijcmp.2.2.2

Download | Downloads : 6 | Total View : 1871

Share

In this paper, we provide the solution of a modeled parallel resonant circuit using the decomposition method. The parallel resonant circuit also known as resistor (R) in ohms, inductor (L) in Henry and capacitor (C) in farads (RLC) circuit is used in turning radio or audio receivers. The mathematical models are in a system of ordinary differential equations (ODE), which we solve using the Adomian Decomposition Method (ADM). We discovered that this method gave exact solutions as can be obtained using any traditionally known analytic method. These findings are illustrated in three test problems.

Adomian Decomposition Method, Resonant Circuits, System of Differential equations.

[1] A. Ahmed, “Convergence of Adomian Decomposition Method for Initial Value Problems”, Numerical Method for Partial Differential Equations, vol. 27, pp. 749 – 752. 2011
[2] E. U. Agom, F. O. Ogunfiditimi, E. V. Bassey ”Lobatto-Runge-Kutta Collocation and Adomian Decomposition Methods On Stiff Differential Equations” International Journal of Mathematical Research, vol. 6, No. 2, pp. 53-59, December 2017.
[3] E. U. Agom, F. O. Ogunfiditimi, E. V. Bassey, “Numerical Application of Adomian Decomposition Method to Fifth-Order Autonomous Differential Equations” Journal of Mathematics and Computer Science, vol. 7, No. 3, pp. 554-563, May 2017.
[4] E. U. Agom, F. O. Ogunfiditimi, P. N. Assi, “Multistage Adomian Decomposition Methods for Nonlinear 4th Order Multi-point Boundary Value Problems” Global Journal of Mathematics, vol. 10, No. 2, pp. 675-680, July 2017.
[5] E. U. Agom, F. O. Ogunfiditimi, P. N. Assi, “On Adomian Polynomial and its Application to Lane-Emden Type of Equation” International Journal of Mathematical Research, vol. 6, No. 1, pp. 13-21, April 2017.
[6] G. Adomian, Solving Frontier Problems in Physics: The Decomposition Method, New York, Springer
[7] I. Gregory, K. Arkadiy, B. Sam, “An RC Load Model of Parallel and Series Parallel Resonant DC-DC Converter with Output Filter” IEEE Transactions On Power Electronics, vol. 14, No 3, pp. 515–521, May 1999.
[8] L. H. Loomis “Ordinary Differential Equations: Introductory and Intermediate Courses Using Matrix Methods”, Adddison-Wesley Publishing Company, Boston, 1971.
[9] T. W. Tushar, S. B. Votthal, “Mathematical Model, Design and Analysis of LLC-T Series Parallel Resonant Converter” IOSR Journal of Electronic and Communication Engineering (IOSR-JECE), vol. 14, pp. 19–25,
[10] W. Janusz, J. Agnieszka, “Analysis of Parallel Resonance Circuit with Supercapacitor” Pozan University of Technology Academic Journal, No 77, pp. 93–99, 2014.
[11] Y. Cherruault, G. Adomian, K. Abbaoui, R. Rach, “Further Remarks on Convergence of Decomposition”, International Journal of Bio-Medical Computing, vol. 38, pp. 89-93, 1995.