Analytical solutions of nonlinear schrodinger equations using multistep modified reduced differential transform method

Authors

  • Hussin CHC Preparatory Centre of Science and Technology, Universiti Malaysia Sabah, Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia
  • Kilicman A Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang Selangor, Malaysia
  • Azmi A School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

Keywords:

Adomian polynomials, multistep approach, Reduced Differential Transform Method, nonlinear Schrodinger equations

Abstract

This paper aims to propose and implement the Multistep Modified Reduced Differential Transform Method (MMRDTM) to find solution of Nonlinear Schrodinger Equations (NLSEs). Through the proposed technique, we replaced the nonlinear term in the NLSEs by the corresponding Adomian polynomials prior applying the multistep approach. Thus, we can obtain solutions for the NLSEs in easier way with less complexity. In addition, the solutions can be approximated more accurately over a longer time frame. We considered several NLSEs and illustrate the features of these solutions in the form of graphs in order to show the power and accuracy of the MMRDTM.

References

Islam, R., Khan, K., Akbar, M. A., Islam, M. E., & Ahmed, M. T, "Traveling wave solutions of some nonlinearevolution equations." Alexandria Engineering Journal, 54(2), (2015): 263–269.

Seadawy, A. R., “Exact solutions of a two-dimensional nonlinear Schrdinger equation.”Applied Mathematics Letters, 25(4), 2012):687–691.

Sadighi, A., & Ganji, D. D. ,”Analytic treatment of linear and nonlinear Schrödinger equations: A study withhomotopyperturbation and Adomian decomposition methods.” Physics Letters, Section A: General, Atomic and Solid State Physics, 372(4), (2008):465–469.

Biazar, J., & Ghazvini, H., “Exact solutions for non-linear Schrödinger equations by He’s homotopyperturbation method.”Physics Letters, Section A: General, Atomic and Solid State Physics, 366(1–2),(2007): 79–84.

Bratsos, A., Ehrhardt, M., & Famelis, I. T.,”A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations.” Applied Mathematics and Computation, 197(1), (2008): 190–205.

Wazwaz, A. M., “A study on linear and nonlinear Schrodinger equations by the variational iteration method.”Chaos, Solitons and Fractals, 37(4),(2008): 1136–1142.

Ravi Kanth, A. S. V, & Aruna, K.,“Two-dimensional differential transform method for solving linear and non-linear Schrödinger equations.”Chaos, Solitons and Fractals, 41(5),(2009): 2277–2281.

Taghizadeh, N., & Noori, S. R. M. ,”Exact Solutions of the Cubic Nonlinear Schrodinger Equation with a Trapping Potential by Reduced Differential Transform Method.”Math. Sci. Lett.,5(3),(2016):1-5.

Jameel A.F., Anakira N.R., Rashidi M. M., Alomari A.K., Saaban A., Shakhatreh M. A.,“DifferentialTransformation Method For Solving High Order Fuzzy Initial Value Problems.”Italian Journal of Pure and Applied Mathematics, 39,(2018): 194–208.

Rao, T. R. R.,“Numerical Solution of Sine Gordon Equations Through Reduced Differential Transform Method.”Global Journal of Pure and Applied Mathematics, 13(7), (2017):3879–3888.

Acan, O., & Keskİn, Y.,”Reduced Differential Transform Method for ( 2 + 1 ) Dimensional type of the Zakharov – Kuznetsov ZK ( n ,

n ) Equations.”AIP Conference Proceedings,1648(1),(2015).

Marasi, H. R., Sharifi, N., & Piri, H.,”Modified differential transform method for singular Lane-Emden equations in integer and fractional order”, Journal of Applied and Engineering Mathematics, 5(1),(2015): 124–131.

Benhammouda, B., & Leal, H. V., “A new multi ‑ step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.”SpringerPlus, 5(1), (2016):1723.

Ray, S. S., “Numerical Solutions and Solitary Wave Solutions of Fractional KdV Equations using Modified Fractional Reduced Differential Transform Method.”Journal of Mathematical Chemistry, 51(8),(2013): 2214–2229.

El-Zahar, E. R.,“Applications of adaptive multi step differential transform method to singular perturbation problems arising in science and engineering.”Applied Mathematics and Information Sciences, 9(1), (2015): 223–232.

Keskin, Y., & Oturanç, G.,”Reduced differential transform method for partial differential equations.”International Journal of Nonlinear

Sciences and Numerical Simulation, 10(6),(2009): 741–749.

Downloads

Published

2024-02-26

How to Cite

Hussin, C. H. C., Kilicman, A., & Azmi, A. (2024). Analytical solutions of nonlinear schrodinger equations using multistep modified reduced differential transform method. COMPUSOFT: An International Journal of Advanced Computer Technology, 7(11), 2939–2944. Retrieved from https://ijact.in/index.php/j/article/view/464

Issue

Section

Original Research Article

Similar Articles

<< < 14 15 16 17 18 19 20 21 22 23 > >> 

You may also start an advanced similarity search for this article.