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An analytical technique for solving general linear integral equations of the second kind and its application in analysis of flash lamp control circuit

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Języki publikacji
EN
Abstrakty
EN
In this paper an application of the homotopy perturbation method for solving the general linear integral equations of the second kind is discussed. It is shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in the homotopy perturbation method is convergent. The error of approximate solution, received by taking only the partial sum of the series, is also estimated. Moreover, there is presented an example of applying the method for approximate solution of an equation which has a practical application for charge calculation in supply circuit of the flash lamps used in cameras.
Rocznik
Strony
413--421
Opis fizyczny
Bibliogr. 41 poz., rys., tab., wykr.
Twórcy
autor
  • Institute of Mathematics, Silesian University of Technology, 23 Kaszubska St., 44-100 Gliwice, Poland
autor
  • Institute of Mathematics, Silesian University of Technology, 23 Kaszubska St., 44-100 Gliwice, Poland
  • Department of Mechatronics, Faculty of Electrical Engineering, Silesian University of Technology, 10A Akademicka St., 44-100 Gliwice, Poland, tomasz.trawinski@polsl.pl
autor
  • Institute of Mathematics, Silesian University of Technology, 23 Kaszubska St., 44-100 Gliwice, Poland
Bibliografia
  • [1] J.-H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems”, Int. J. Non-Linear Mech. 35, 37–43 (2000).
  • [2] J.-H. He, “Some asymptotic methods for strongly nonlinear equations”, Int. J. Modern Phys. B 20, 1141–1199 (2006).
  • [3] J.-H. He, Non-Perturbative Methods for Strongly Nonlinear Problems, Dissertation.de Verlag, Berlin, 2006.
  • [4] M. Dehghan and F. Shakeri, “Solution of a partial differential equation subject to temperature overspecification by He’s homotopy perturbation method”, Phys. Scr. 75, 778–787 (2007).
  • [5] F. Shakeri and M. Dehghan, “Inverse problem of diffusion equation by He’s homotopy perturbation method”, Phys. Scr. 75, 551–556 (2007).
  • [6] J. Biazar and H. Ghazvini, “Homotopy perturbation method for solving hyperbolic partial differential equations”, Comput. Math. Appl. 56, 453–458 (2008).
  • [7] C. Chun, H. Jafari, and Y.-I. Kim, “Numerical method for the wave and nonlinear diffusion equations with the homotopy perturbation method”, Comput. Math. Appl. 57, 1226–1231 (2009).
  • [8] A. Sadighi and D.D. Ganji, “Exact solutions of Laplace equation by homotopy-perturbation and Adomian decomposition methods”, Phys. Lett. A 367, 83–87 (2007).
  • [9] A. Yildirim, “Analytical approach to fractional partial differential equations in fluid mechanics by means of the homotopy perturbation method”, Int. J. Numer. Methods Heat Fluid Flow 20, 186–200 (2010).
  • [10] M. Madani, M. Fathizadeh, Y. Khan, and A. Yildirim, “On the coupling of the homotopy perturbation method and Laplace transformation”, Math. Comput. Modelling 53, 1937–1945 (2011).
  • [11] Y. Khan, M. Akbarzade, and A. Kargar, “Coupling of homotopy and variational approach for conservative oscillator with strong odd-nonlinearity”, Sci. Iran. 19, 417–422 (2012).
  • [12] M. Dehghan and J. Heris, “Study of the wave-breaking’s qualitative behavior of the Fornberg-Whitham equation via quasinumeric approaches”, Int. J. Numer. Methods Heat Fluid Flow 22, 537–553 (2012).
  • [13] D.D. Ganji, A. Rajabi, “Assessment of homotopy-perturbation and perturbation methods in heat radiation equations”, Int. Comm. Heat & Mass Transf. 33, 391–400 (2006).
  • [14] D.D. Ganji, M.J. Hosseini, and J. Shayegh, “Some nonlinear heat transfer equations solved by three approximate methods”, Int. Comm. Heat & Mass Transf. 34, 1003–1016 (2007).
  • [15] D.D. Ganji, G.A. Afrouzi, and R.A. Talarposhti, “Application of variational iteration method and homotopy-perturbation method for nonlinear heat diffusion and heat transfer equations”, Phys. Lett. A 368, 450–457 (2007).
  • [16] H. Khaleghi, D.D. Ganji, and A. Sadighi, “Application of variational iteration and homotopy-perturbation methods to nonlinear heat transfer equations with variable coefficients”, Numer. Heat Transfer A 52, 25–42 (2007).
  • [17] A. Rajabi, D.D. Ganji, and H. Taherian, “Application of homotopy perturbation method in nonlinear heat conduction and convection equations”, Phys. Lett. A 360, 570–573 (2007).
  • [18] D. Słota, “The application of the homotopy perturbation method to one-phase inverse Stefan problem”, Int. Comm. Heat & Mass Transf. 37, 587–592 (2010).
  • [19] D. Słota, “Homotopy perturbation method for solving the twophase inverse Stefan problem”, Numer. Heat Transfer A 59, 755–768 (2011).
  • [20] E. Hetmaniok, I. Nowak, D. Słota, and R. Wituła, “Application of the homotopy perturbation method for the solution of inverse heat conduction problem”, Int. Comm. Heat & Mass Transf. 39, 30–35 (2012).
  • [21] R. Grzymkowski, E. Hetmaniok, and D. Słota, “Application of the homotopy perturbation method for calculation of the temperature distribution in the cast-mould heterogeneous domain”, J. Achiev. Mater. Manuf. Eng. 43, 299–309 (2010).
  • [22] J. Biazar and H. Ghazvini, “Convergence of the homotopy perturbation method for partial differential equations”, Nonlinear Anal.: Real World Appl. 10, 2633–2640 (2009).
  • [23] J. Biazar and H. Aminikhah, “Study of convergence of homotopy perturbation method for systems of partial differential equations”, Comput. Math. Appl. 58, 2221–2230 (2009).
  • [24] M. Turkyilmazoglu, “Convergence of the homotopy perturbation method”, Int. J. Nonlin. Sci. Numer. Simulat. 12, 9–14 (2011).
  • [25] S. Abbasbandy, “Numerical solutions of the integral equations: Homotopy perturbation method and Adomian’s decomposition method”, Appl. Math. Comput. 173, 493–500 (2006).
  • [26] M. Ghasemi, M.T. Kajani, and A. Davari, “Numerical solution of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method”, Appl. Math. Comput. 188, 446–449 (2007).
  • [27] A. Golbabai and M. Javidi, “Application of He’s homotopy perturbation method for nth-order integro-differential equations”, Appl. Math. Comput. 190, 1409–1416 (2007).
  • [28] A. Ghorbani and J. Saberi-Nadjafi, “Exact solutions for nonlinear integral equations by a modified homotopy perturbation method”, Comput. Math. Appl. 56, 1032–1039 (2008).
  • [29] M. Dehghan and F. Shakeri, “Solution of an integro-differential equation arising in oscillating megnetic fields using He’s homotopy perturbation method”, Prog. Electromagnetics Research, PIER 78, 361–376 (2008).
  • [30] A. Alawneh, K. Al-Khaled, and M. Al-Towaiq, “Reliable algorithms for solving integro-differential equations with applications”, Int. J. Comput. Math. 87, 1538–1554 (2010).
  • [31] J. Biazar, Z. Ayati, and M.R. Yaghouti, “Homotopy perturbation method for homogeneous Smoluchowski’s equation”, Numer. Methods Partial Differential Equations 26, 1146–1153 (2010).
  • [32] H. Jafari, M. Alipour, and H. Tajadodi, “Convergence of homotopy perturbation method for solving integral equations”, Thai J. Math. 8, 511–520 (2010).
  • [33] H. Aminikhah and J. Biazar, “A new analytical method for solving systems of Volterra integral equations”, Int. J. Comput. Math. 87, 1142–1157 (2010).
  • [34] E. Babolian and N. Dastani, “Numerical solutions of twodimensional linear and nonlinear Volterra integral equation: homotopy perturbation method and differential transform method”, Int. J. Ind. Math. 3, 157–167 (2011).
  • [35] J. Biazar, B. Ghanbari, M.G. Porshokouhi, and M.G. Porshokouhi, “He’s homotopy perturbation method: A strongly promising method for solving non-linear systems of the mixed Volterra-Fredholm integral equations”, Comput. Math. Appl. 61, 1016–1023 (2011).
  • [36] Z. Chen and W. Jiang, “Piecewise homotopy perturbation method for solving linear and nonlinear weakly singular VIE of second kind”, Appl. Math. Comput. 217, 7790–7798 (2011).
  • [37] E. Hetmaniok, D. Słota, and R. Wituła, “Convergence and error estimation of homotopy perturbation method for Fredholm and Volterra integral equations”, Appl. Math. Comput. 218, 10717–10725 (2012).
  • [38] E. Hetmaniok, I. Nowak, D. Słota, and R. Wituła, “A study of the convergence of and error estimation for the homotopy perturbation method for the Volterra-Fredholm integral equations”, Appl. Math. Lett. 26, 165–169 (2013).
  • [39] J.C. Campo, M.A. Pkrez, J.M. Mezquita, and J. Sebastian, “Circuit-design criteria for improvement of xenon flash-lamp performance (lamp life, light-pulse, narrowness, uniformity of light intensity in a series of flashes)”, Applied Power Electronics Conference and Exposition, APEC’97, Twelfth Annual, vol. 2, 1057–1061 (1997).
  • [40] W. Janke, “Equivalent circuits for averaged description of DCDC switch-mode power converters based on separation of variables approach”, Bull. Pol. Ac.: Tech. 61 (3), 711–723 (2013).
  • [41] S. Jalbrzykowski and T. Citko, “Push-pull resonant DC-DC isolated converter”, Bull. Pol. Ac.: Tech. 61 (4), 763–769 (2013).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-71745edf-6d88-41ce-bb14-d780628a0c0f
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