A study on linear and non linear Schrodinger equations by reduced differential transform method

Downloads

DOI:

https://doi.org/10.26637/mjm401/008

Abstract

In this paper, reduced differential transform method (RDTM) is used to obtain the exact solution of nonlinear Schrodinger equation. Compared to other existing analytical/numerical methods, RDTM is more efficient and easy to apply.

Keywords:

Non-linear Schrodinger equations, reduced differential transform, reduced differential inverse transform, analytic solution

Mathematics Subject Classification:

35J10, 35F25
  • T.R. Ramesh Rao Department of Mathematics and Actuarial Science, B.S. Abdur Rahman University, Chennai-600 048, TamilNadu, India.
  • Pages: 59-64
  • Date Published: 01-01-2016
  • Vol. 4 No. 01 (2016): Malaya Journal of Matematik (MJM)

Mousa MM, Ragab SF, Application of the homotopy perturbation method to linear and nonlinear Schrodinger equation, Z. Naturforsch. Sect. A 63 (2008), 140-144. DOI: https://doi.org/10.1515/zna-2008-3-404

Wazwaz AM, A study on linear and nonlinear Schrodinger equations by variation iteration method, Chaos, Solitons and Fractals, 37 (2008), 1136-1142. DOI: https://doi.org/10.1016/j.chaos.2006.10.009

Ravikanth ASV, Aruna K, Two dimensional differential transform method for solving linear and nonlinear Schrodinger equations, Chaos, Solitons and Fractals, 41 (2009), 2277-2281. DOI: https://doi.org/10.1016/j.chaos.2008.08.037

Wang $mathrm{H}$, Numerical studies on the split-step finite difference method for nonlinear Schrodinger equation, Appl. Math. Comput., 170 (2005), 17-35. DOI: https://doi.org/10.1016/j.amc.2004.10.066

Biazar J, Ghazvini H, Exact solution for Schrodinger equations by Hes homotopy perturbation method, Phys. Let. A 366 (2007), 79-84. DOI: https://doi.org/10.1016/j.physleta.2007.01.060

Sadighi A, Ganji DD, Analytic treatment of linear and nonlinear Schrodinger equation: A study with homotopy perturbation and Adomian decomposition methods, Phys. Lett A. 372 (2008), 465-9. DOI: https://doi.org/10.1016/j.physleta.2007.07.065

Borhanifar A, Reza Abazari, Exact solutions for nonlinear Schrodinger equation by differential transform method, J. Appl. Math. Comput., 35 (2011), 37-51. DOI: https://doi.org/10.1007/s12190-009-0338-2

Alomari AK, Noorani MSM, Wazar R, Explicit series solutions of some linear and nonlinear Schrodinger equations via the homotopy analysis method, Commun. Nonlinear Sci-Numer. Simul. (2008). DOI: https://doi.org/10.1016/j.cnsns.2008.01.008

Khuri SA, A new approach to the cubic Schrodinger equation: an application of the decomposition technique, Appl. Math. Comput., 97 (1998), 251-254. DOI: https://doi.org/10.1016/S0096-3003(97)10147-3

Srivastava VK, Nachiketa Mishra, Sunil kumar, Brajesh kumar singh, Aswathi MK, Reduced differential transform method for solving $(n+1)$-Dimensional Burgers equations, Egyptian journal of Basic and Applied sciences, 1 (2014), 115-119. DOI: https://doi.org/10.1016/j.ejbas.2014.05.001

Keskin Y, Galip Oturanc, Reduced differential transform method for partial differential equations, Int. Journal of nonlinear sciences and numerical simulation, 10(6) (2009), 741-749. DOI: https://doi.org/10.1515/IJNSNS.2009.10.6.741

Keskin Y, Galip Oturanc, Reduced differential transform method for generalized KdV equations, Math. Comput. Appl., 15(3) (2010), 382-393. DOI: https://doi.org/10.3390/mca15030382

Keskin Y, Ph.D Thesis, Selcuk University, 2010 (in Turkish).

Brahim Benhammouda, Hector Vazquez-Leal, Arturo Sarmiento-Reyes, Modified Reduced Differential transform method for partial differential - algebraic equations, Journal of applied mathematics, 2014, 1-9, Article ID 279481. DOI: https://doi.org/10.1155/2014/279481

Saravanan A, Magesh N, A comparison between the reduced differential transform method and the Adomian decomposition method for the Newell-Whitehead-Segel equation, Journal of Egyptian mathematical society, 21 (2013), 259-265. DOI: https://doi.org/10.1016/j.joems.2013.03.004

Abazari R, Abazari M, Numerical study of Burgers-Huxley equations via reduced differential transform method, Comput. Appl. Math., 32(1) (2013), 1-17. DOI: https://doi.org/10.1007/s40314-013-0001-2

Abazari R, Abazari M, Numerical simulation of generalized Hirota-Satsuma coupled KdV equation by RDTM and comparison with DTM, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 619-629. DOI: https://doi.org/10.1016/j.cnsns.2011.05.022

  • NA

Metrics

PDF views
98
Jan 2016Jul 2016Jan 2017Jul 2017Jan 2018Jul 2018Jan 2019Jul 2019Jan 2020Jul 2020Jan 2021Jul 2021Jan 2022Jul 2022Jan 2023Jul 2023Jan 2024Jul 2024Jan 2025Jul 2025Jan 202612
|

Published

01-01-2016

How to Cite

T.R. Ramesh Rao. “A Study on Linear and Non Linear Schrodinger Equations by Reduced Differential Transform Method”. Malaya Journal of Matematik, vol. 4, no. 01, Jan. 2016, pp. 59-64, doi:10.26637/mjm401/008.
Yun-Ho Kim (2020)
Existence and Multiplicity of Solutions to a Class of Fractional p-Laplacian Equations of Schrödinger-Type with Concave-Convex Nonlinearities in ℝN. Mathematics, 8(10), 1792.
10.3390/math8101792
Kisoeb Park (2022)
Multiplicity Results of Solutions to Non-Local Magnetic Schrödinger–Kirchhoff Type Equations in RN. Axioms, 11(2), 38.
10.3390/axioms11020038
Sita Charkrit (2025)
A reliable algorithm for solving higher order schrödinger equations with enhanced convergence. Partial Differential Equations in Applied Mathematics, 13, 101147.
10.1016/j.padiff.2025.101147