Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation
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 (...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6626236 |
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| author | Metomou Richard Weidong Zhao |
| author_facet | Metomou Richard Weidong Zhao |
| author_sort | Metomou Richard |
| collection | DOAJ |
| description | 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 PL/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. |
| format | Article |
| id | doaj-art-28a3375cabbd4bb280812e3120088e8d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-28a3375cabbd4bb280812e3120088e8d2025-02-03T05:49:27ZengWileyJournal of Applied Mathematics1110-757X1687-00422021-01-01202110.1155/2021/66262366626236Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger EquationMetomou Richard0Weidong Zhao1School of Mathematics, Shandong University, ChinaSchool of Mathematics, Shandong University, ChinaThe 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 PL/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.http://dx.doi.org/10.1155/2021/6626236 |
| spellingShingle | Metomou Richard Weidong Zhao Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation Journal of Applied Mathematics |
| title | Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation |
| title_full | Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation |
| title_fullStr | Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation |
| title_full_unstemmed | Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation |
| title_short | Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation |
| title_sort | pade sumudu adomian decomposition method for nonlinear schrodinger equation |
| url | http://dx.doi.org/10.1155/2021/6626236 |
| work_keys_str_mv | AT metomourichard padesumuduadomiandecompositionmethodfornonlinearschrodingerequation AT weidongzhao padesumuduadomiandecompositionmethodfornonlinearschrodingerequation |