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Padé‐Sumudu‐Adomian Decomposition Method for Nonlinear Schrödinger Equation

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Listed:
  • Metomou Richard
  • Weidong Zhao

Abstract

The main purpose of this paper is to solve the nonlinear Schrödinger equation using some suitable analytical and numerical methods such as Sumudu transform, Adomian Decomposition Method (ADM), and Padé approximation technique. In many literatures, we can see the Sumudu Adomian decomposition method (SADM) and the Laplace Adomian decomposition method (LADM); the SADM and LADM provide similar results. The SADM and LADM methods have been applied to solve nonlinear PDE, but the solution has small convergence radius for some PDE. We perform the SADM solution by using the function P[L/M][·] called double Padé approximation. We will provide the graphical numerical simulations in 3D surface solutions of each application and the absolute error to illustrate the efficiency of the method. In our methods, the nonlinear terms are computed using Adomian polynomials, and the Padé approximation will be used to control the convergence of the series solutions. The suggested technique is successfully applied to nonlinear Schrödinger equations and proved to be highly accurate compared to the Sumudu Adomian decomposition method.

Suggested Citation

  • Metomou Richard & Weidong Zhao, 2021. "Padé‐Sumudu‐Adomian Decomposition Method for Nonlinear Schrödinger Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnljam:v:2021:y:2021:i:1:n:6626236
    DOI: 10.1155/2021/6626236
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    References listed on IDEAS

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    1. Fethi Bin Muhammed Belgacem & Ahmed Abdullatif Karaballi, 2006. "Sumudu transform fundamental properties investigations and applications," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-23, May.
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