Accès libre

Approximate Solution of Painlevé Equation I by Natural Decomposition Method and Laplace Decomposition Method

, , ,  et   
15 juil. 2023
À propos de cet article

Citez
Télécharger la couverture

Painleve P. Sur les équationsdifférentielles du second ordre et d’ordresupérieurdontl’intégralegénéraleestuniforme. Acta mathematica. 1902 Dec;25:1-85. Search in Google Scholar

Borisov AV, Kudryashov NA. Paul Painlevé and his contribution to science. Regular and Chaotic Dynamics. 2014 Feb;19:1-9. Search in Google Scholar

Segur H, Ablowitz MJ. Asymptotic solutions of nonlinear evolution equations and a Painlevé transcedent. Physica D: Nonlinear Phenomena. 1981 Jul 1;3(1-2):165-84. Search in Google Scholar

Kanna T, Sakkaravarthi K, Kumar CS, Lakshmanan M, Wadati M. Painlevé singularity structure analysis of three component Gross– Pitaevskii type equations. Journal of mathematical physics. 2009 Nov 25;50(11):113520. Search in Google Scholar

Cao X, Xu C. ABäcklund transformation for the Burgers hierarchy. InAbstract and Applied Analysis 2010 Jan 1 (Vol. 2010). Hindawi. Search in Google Scholar

Lee SY, Teodorescu R, Wiegmann P. Viscous shocks in Hele–Shaw flow and Stokes phenomena of the Painlevé I transcendent. Physica D: Nonlinear Phenomena. 2011 Jun 15;240(13):1080-91. Search in Google Scholar

Dai D, Zhang L. On tronquée solutions of the first Painlevé hierarchy. Journal of Mathematical Analysis and Applications. 2010 Aug 15;368(2):393-9. Search in Google Scholar

]Florjańczyk M, Gagnon L. Exact solutions for a higher-order nonlinear Schrödinger equation. Physical Review A. 1990 Apr 1;41(8):4478. Search in Google Scholar

Ablowitz MJ, Segur H. Solitons and the inverse scattering transform. Society for Industrial and Applied Mathematics; 1981 Jan 1. Search in Google Scholar

Tajiri M, Kawamoto S. Reduction of KdV and cylindrical KdV equations to Painlevé equation. Journal of the Physical Society of Japan. 1982 May 15;51(5):1678-81. Search in Google Scholar

Dehghan M, Shakeri F. The numerical solution of the second Painlevé equation. Numerical Methods for Partial Differential Equations: An International Journal. 2009 Sep;25(5):1238-59. Search in Google Scholar

Clarkson PA. Special polynomials associated with rational solutions of the fifth Painlevé equation. Journal of computational and applied mathematics. 2005 Jun 1;178(1-2):111-29. Search in Google Scholar

El-Gamel M, Behiry SH, Hashish H. Numerical method for the solution of special nonlinear fourth-order boundary value problems. Applied Mathematics and Computation. 2003 Dec 25;145(2-3):717-34. Search in Google Scholar

Ellahi R, Abbasbandy S, Hayat T, Zeeshan A. On comparison of series and numerical solutions for second Painlevé equation. Numerical Methods for Partial Differential Equations. 2010 Sep;26(5): 1070-8. Search in Google Scholar

Gromak VI, Laine I, Shimomura S. Painlevé differential equations in the complex plane. InPainlevé Differential Equations in the Complex Plane 2008 Aug 22. de Gruyter. Search in Google Scholar

Bobenko AI, Eitner U, editors. Painlevé equations in the differential geometry of surfaces. Berlin, Heidelberg: Springer Berlin Heidelberg; 2000 Dec 12. Search in Google Scholar

Dehghan M, Shakeri F. The numerical solution of the second Painlevé equation. Numerical Methods for Partial Differential Equations: An International Journal. 2009 Sep;25(5):1238-59. Search in Google Scholar

Saadatmandi A. Numerical study of second Painlevé equation. Comm. Numer. Anal. 2012;2012. Search in Google Scholar

Sierra-Porta D, Núnez LA. On the polynomial solution of the first Painlevé equation. Int. J. of Applied Mathematical Research. 2017;6(1):34-8. Search in Google Scholar

Ahmad H, Khan TA, Yao S. Numerical solution of second order Painlevé differential equation. Journal of Mathematics and Computer Science. 2020;21(2):150-7. Search in Google Scholar

Izadi M. An approximation technique for first Painlevé equation. Search in Google Scholar

Khan ZH, Khan WA. N-transform properties and applications. NUST journal of engineering sciences. 2008 Dec 31;1(1):127-33. Search in Google Scholar

Belgacem FB, Silambarasan R. Theory of natural transform. Math. Engg. Sci. Aeros. 2012 Feb 25;3:99-124. Search in Google Scholar

Spiegel MR. Laplace transforms. New York: McGraw-Hill; 1965. Search in Google Scholar

Belgacem FB, Karaballi AA. Sumudu transform fundamental properties investigations and applications. International Journal of Stochastic Analysis. 2006;2006. Search in Google Scholar

Maitama S, Hamza YF. An analytical method for solving nonlinear sine-Gordon equation. Sohag Journal of Mathematics. 2020;7(1):5-10. Search in Google Scholar

Elbadri M, Ahmed SA, Abdalla YT, Hdidi W. A new solution of time-fractional coupled KdV equation by using natural decomposition method. InAbstract and Applied Analysis 2020 Sep 1 (Vol. 2020, pp. 1-9). Hindawi Limited. Search in Google Scholar

Maitama S, Kurawa SM. An efficient technique for solving gas dynamics equation using the natural decomposition method. InInternational Mathematical Forum 2014 (Vol. 9, No. 24, pp. 1177-1190). Hikari, Ltd.. Search in Google Scholar

Amir M, Awais M, Ashraf A, Ali R, Ali Shah SA. Analytical Method for Solving Inviscid Burger Equation. Punjab University Journal of Mathematics. 2023 Dec 3;55(1). Search in Google Scholar

Behzadi SS. Convergence of iterative methods for solving Painlevé equation. Applied Mathematical Sciences. 2010;4(30):1489-507. Search in Google Scholar

Hesameddini E, Peyrovi A. The use of variational iteration method and homotopy perturbation method for Painlevé equation I. Applied Mathematical Sciences. 2009;3(37-40):1861-71. Search in Google Scholar

Behzadi SS. Convergence of iterative methods for solving Painlevé equation. Applied Mathematical Sciences. 2010;4(30):1489-507. Search in Google Scholar