Abstract
This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a wide time frame. Two examples are provided for showing the ability and advantages of the proposed method to approximate the solution of the power law nonlinearity of NLSEs. For pictorial representation, graphical inputs are included to represent the solution and show the precision as well as the validity of the MMRDTM.
Highlights
The nonlinear nature of the system is vital especially for understanding numerous natural phenomena
Multistep Modified Reduced Differential Transform Method (MMRDTM) for solving nonlinear Schrödinger equations (NLSEs) is proposed by Che Hussin et al [17]
The series of solutions of NLSEs of power law nonlinearity using MMRDTM is successfully applied in this paper
Summary
The nonlinear nature of the system is vital especially for understanding numerous natural phenomena. The nonlinear Schrödinger equations (NLSEs) serve as a critical function in various areas of engineering, biological and physical science These equations are applicable in some applied fields such as protein chemistry, plasma physics, nonlinear optics, and liquid dynamics [6]. Apart from that, Ray proposed a modification on the fractional RDTM and implemented it to find solutions of fractional Korteweg-de Vries equations [15] In this approach, the adjustment embraces the substitution of the nonlinear term by relating Adomian polynomials. Multistep Modified Reduced Differential Transform Method (MMRDTM) for solving NLSEs is proposed by Che Hussin et al [17]. By using this method, the solutions of NLSE can be approximated with high accuracy. The number of computed terms is significantly reduced
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