Preferences help
enabled [disable] Abstract
Number of results
2021 | 154 | 152-174
Article title

Series Solution of Nonlinear Ordinary Differential Equations Using Single Laplace Transform Method in Mathematical Physics

Title variants
Languages of publication
In this paper, a novel technique is created to enable the extension of the single Laplace transform method (SLTM) to solve nonlinear ordinary differential equations (ODEs) is presented. The main parts of the recommended technique are the Adomian polynomials. By developing several theorems, which include the Laplace transformation of nonlinear expressions, the Adomian polynomials are made possible. Several famous nonlinear equations including the Blasius equation, the Poisson Boltzmann equation, and numerous extra problems relating nonlinearities of many types such as exponential and sinusoidal are resolved for description. As it was revealed in the specified equations, and problems, our technique is conceptually and computationally simple. Some nonlinear examples are taken from the literature for checking the validation and convergence of the proposed technique. The suggested method is methodical, precise, then restricted to integration.
Physical description
  • Department of Physics, Imo State University, Owerri, Nigeria
  • Department of Physics, Federal University of Technology, Owerri, Nigeria
  • Department of Information and Communications Technology, Imo State University, Owerri, Nigeria
  • [1] T.H. Glisson. Introduction to Circuit Analysis and Design, Springer, New York, 2011.
  • [2] K. Ogata. Modern Control Engineering, Prentice Hall, New York, 2009.
  • [3] Fatoorehchi, H., & Abolghasemi, H. (2016). Series solution of nonlinear differential equations by a novel extension of the Laplace transform method. International Journal of Computer Mathematics, 93(8), 1299-1319
  • [4] Y. Khan, H. Vázquez-Leal, and N. Faraz. An auxiliary parameter method using Adomian polynomials and Laplace transformation for nonlinear differential equations. Appl. Math. Model. 37 (2013), 2702-2708, MR 3020448
  • [5] S. Abbasbandy. Numerical solutions of the integral equations: Homotopy perturbation method and Adomian’s decomposition method. Appl. Math. Comput. 173 (2006), pp. 493-500, MR 2203403
  • [6] S. Abbasbandy and M.T. Darvishi. A numerical solution of Burgers’ equation by modified Adomian method. Appl. Math. Comput. 163 (2005), 1265–1272, MR 2199478
  • [7] Y. Çenesiz and A. Kurnaz. Adomian decomposition method by Gegenbauer and Jacobi polynomials. Int.J. Comput. Math. 88 (2011), 3666-3676, MR 2853262
  • [8] A. Fakharian, M.T. Hamidi Beheshti, and A. Davari. Solving the Hamilton–Jacobi–Bellman equation using Adomian decomposition method, Int. J. Comput. Math. 87 (2010), 2769-2785, MR 2728206
  • [9] H. Fatoorehchi and H. Abolghasemi. Adomian decomposition method to study mass transfer from a horizontal flat plate subject to laminar fluid flow. Adv. Nat. Appl. Sci. 5 (2011) 26-33
  • [10] H. Fatoorehchi and H. Abolghasemi. Investigation of nonlinear problems of heat conduction in tapered cooling fins via symbolic programming. Appl. Appl. Math. 7 (2012) 717-734, MR 3006674
  • [11] H. Fatoorehchi and H. Abolghasemi. A more realistic approach toward the differential equation governing the glass transition phenomenon. Intermetallics 32 (2012), 35-38
  • [12] H. Fatoorehchi and H. Abolghasemi. Improving the differential transform method: A novel technique to obtain the differential transforms of nonlinearities by the Adomian polynomials. Appl. Math. Model. 37 (2013), 6008-6017, MR 3028446
  • [13] H. Fatoorehchi and H. Abolghasemi. Approximating the minimum reflux ratio of multicomponent distillation columns based on the Adomian decomposition method. J. Taiwan Inst. Chem. E. 45 (2014), 880-886
  • [14] H. Fatoorehchi and H. Abolghasemi. On computation of real eigenvalues of matrices via the Adomian decomposition. J. Egyptian Math. Soc. 22 (2014) 6-10, MR 3168583
  • [15] H. Fatoorehchi and H. Abolghasemi. Finding all real roots of a polynomial by matrix algebra and the Adomian decomposition method. J. Egyptian Math. Soc. 22 (2014) 524–528, MR 3260803
  • [16] H. Fatoorehchi, H. Abolghasemi, and R. Rach. An accurate explicit form of the Hankinson–Thomas– Phillips correlation for prediction of the natural gas compressibility factor. J. Petrol. Sci. Eng. 117 (2014), 46-53
  • [17] B. Kundu and D. Bhanja. Performance and optimization analysis of a constructal T-shaped fin subject to variable thermal conductivity and convective heat transfer coefficient. Int. J. Heat Mass Transf. 53 (2010) 254-267
  • [18] B. Kundu and S. Wongwises. A decomposition analysis on convecting–radiating rectangular plate fins for variable thermal conductivity and heat transfer coefficient. J. Franklin Inst. 349 (2012) 966-984, MR 2899321
  • [19] E. Kutafina, Taylor series for the Adomian decomposition method. Int. J. Comput. Math. 88 (2011), pp. 3677-3684, MR 2853263
  • [20] A.M. Siddiqui, M. Hameed, B.M. Siddiqui, and Q.K. Ghori. Use of Adomian decomposition method in the study of parallel plate flow of a third grade fluid. Commun. Nonlinear Sci. Numer. Simul. 15 (2010) 2388-2399, MR 2602723
  • [21] J.-S. Duan. Recurrence triangle for Adomian polynomials. Appl. Math. Comput. 216 (2010) 1235-1241, MR 2607232
  • [22] H. Fatoorehchi and H. Abolghasemi. On calculation of Adomian polynomials by MATLAB. J. Appl. Comput. Sci. Math. 5 (2011) 85-88
Document Type
Publication order reference
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.