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An Integrative Approach for Analysis of Nonlinear Electrical Circuits Using-Polynomial B-Spline Expansion and B-Spline Krawczyk Operator

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Abstract

This paper addresses the problem of finding a set of all direct current (DC) operating points of a nonlinear circuit, which is a crucial step in its development and requires the solution of a nonlinear system of polynomial equations. We propose a novel algorithm for finding the set of all solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n dimensional box. The proposed algorithm is based on the following techniques: (i) B-Spline expansion to obtain a polynomial B-Spline form of the original polynomial in power form; (ii) B-Spline Krawczyk contractor for domain pruning. To avoid the repeated evaluation of function value the algorithm suggested uses B-Spline coefficients to find the value of Krawczyk operator and the computation of derivative of polynomial function. We solved three circuit analysis problems using the proposed algorithm and compared the performance of proposed algorithm with INTLAB-based solver and found that the former is more efficient in terms of computation time and number of iterations.

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References

  1. L. Trajkovic, Nonlinear Theory and Its Applications, IEICE 3(3), 287 (2012)

    MathSciNet  Google Scholar 

  2. Jäger, C., Ratz, D., et al.: Reliable Computing 1(1), 41 (1995)

    Article  MathSciNet  Google Scholar 

  3. Kolev, L.: IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 47(5), 675 (2000)

    Article  Google Scholar 

  4. Nikan, O., Avazzadeh, Z.: Coupling of the Crank–Nicolson scheme and localized meshless technique for viscoelastic wave model in fluid flow. Journal of Computational and Applied Mathematics 398,(2021). https://doi.org/10.1016/j.cam.2021.113695. https://www.sciencedirect.com/science/article/pii/S0377042721003174

  5. Nikan, O., Avazzadeh, Z.: An efficient localized meshless technique for approximating nonlinear sinh-Gordon equation arising in surface theory. Engineering Analysis with Boundary Elements 130, 268 (2021). https://doi.org/10.1016/j.enganabound.2021.05.019. https://www.sciencedirect.com/science/article/pii/S0955799721001466

  6. Nikan, O., Avazzadeh, Z.: A localisation technique based on radial basis function partition of unity for solving Sobolev equation arising in fluid dynamics. Applied Mathematics and Computation 401,(2021).https://doi.org/10.1016/j.amc.2021.126063. https://www.sciencedirect.com/science/article/pii/S0096300321001119

  7. Nikan, O., Avazzadeh, Z., Machado, J.T.: Numerical simulation of a degenerate parabolic problem occurring in the spatial diffusion of biological population. Chaos, Solitons & Fractals 151, 111220 (2021)

    Article  MathSciNet  Google Scholar 

  8. Nikan, O., Avazzadeh, Z., Rasoulizadeh, M.N.: Soliton solutions of the nonlinear sine-Gordon model with Neumann boundary conditions arising in crystal dislocation theory. Nonlinear Dynam. 106(1), 783-813 (2021)

  9. Hammer, R., Hocks, M., Kulisch, U., Ratz, D.: Numerical toolbox for verified computing I: basic numerical problems theory, algorithms, and pascal-XSC programs. 21 (Springer Science & Business Media, 2012)

  10. E. Hansen, G. Walster, Global Optimization Using Interval Analysis Second Edition, Revised and Expanded, vol. 264 (MARCEL DEKKER, INC. New York, 2004)

    Google Scholar 

  11. R.E. Moore, Methods and Applications of Interval Analysis (SIAM, Philadelphia, 1979)

    Book  Google Scholar 

  12. Nataraj, P., Sondur, S.: Construction of bode envelopes using REP based range finding algorithms. International Journal of Automation and Computing 8(1), 112 (2011)

    Article  Google Scholar 

  13. Michel, D., Zidna, A.: in Modelling, Computation and Optimization in Information Systems and Management Sciences, pp. 455–465 (Springer, 2015)

  14. Lin, Q., Rokne, J.: Computers & Mathematics with Applications 31(7), 101 (1996)

    Article  MathSciNet  Google Scholar 

  15. Lin, Q., Rokne, J.: Journal of Computational and Applied Mathematics 58(2), 193 (1995)

    Article  MathSciNet  Google Scholar 

  16. Gawali, D., Zidna, A., Nataraj, P.: Computers & Operations Research 87, 205 (2017)

    Article  MathSciNet  Google Scholar 

  17. Garloff, J.: Interval Computations 6(2), 154 (1993)

    MathSciNet  MATH  Google Scholar 

  18. R. DeVore, G. Lorentz, Constructive Approximation, A Series of Comprehensive Studies in Mathematics (Springer-Verlag, Berline Heidelberg, 1993)

    Book  Google Scholar 

  19. C.K. Shene. CS3621 Introduction to Computing with Geometry Notes. http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/ (2014)

  20. Arounassalame, M.: International Journal of Automation and Computing 9(1), 81 (2012)

    Article  Google Scholar 

  21. Kolev, L.: Interval methods for circuit analysis, 1 (World Scientific, 1993)

  22. Mathworks Inc., MATLAB version 8.0.0.783 (R 2012 b) (Inc., Natick, Massachusetts, United States, 2012)

  23. Rump, S.M.: In Developments in reliable computing, pp. 77-104 (Springer, 1999)

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  1. D. D. Gawali

    Present address: Vidyavardhini’s College of Engineering and Technology, Maharashtra, India

Authors and Affiliations

  1. LGIPM, University of Lorraine, Metz, France

    A. Zidna

  2. Systems and Control Engineering, Indian Institute of Technology, Bombay, India

    P. S. V. Nataraj

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  1. D. D. Gawali
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  2. A. Zidna
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  3. P. S. V. Nataraj
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Correspondence to D. D. Gawali.

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Gawali, D.D., Zidna, A. & Nataraj, P.S.V. An Integrative Approach for Analysis of Nonlinear Electrical Circuits Using-Polynomial B-Spline Expansion and B-Spline Krawczyk Operator. Int. J. Appl. Comput. Math 8, 1 (2022). https://doi.org/10.1007/s40819-021-01198-w

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  • DOI: https://doi.org/10.1007/s40819-021-01198-w

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