Approximate Solutions of Non-linear Fractional Schrodinger Equation Via Differential Transform Method and Modified Differential Transform Method

2013 ◽  
Vol 36 (2) ◽  
pp. 201-213 ◽  
Author(s):  
K. Aruna ◽  
A. S. V. Ravi Kanth
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Transform Method ◽  
Fractional Schrödinger Equation ◽  
Differential Transform ◽  
Non Linear ◽  
Fractional Schrodinger Equation

scholarly journals Modified Fractional Variational Iteration Method for Solving the Generalized Time-Space Fractional Schrödinger Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Baojian Hong ◽  
Dianchen Lu
Keyword(s):  
Schrödinger Equation ◽  
Iteration Method ◽  
Schrodinger Equation ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Fractional Schrödinger Equation ◽  
Variational Iteration ◽  
Time Space ◽  
Generalized Time ◽  
Fractional Schrodinger Equation

Based on He’s variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated. Furthermore, the approximate iterative series and numerical results show that the modified fractional variational iteration method is powerful, reliable, and effective when compared with some classic traditional methods such as homotopy analysis method, homotopy perturbation method, adomian decomposition method, and variational iteration method in searching for approximate solutions of the Schrödinger equations.

scholarly journals Analytical solutions of nonlinear Klein-Gordon equations using Multistep Modified Reduced Differential Transform Method

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 317-326 ◽  
Author(s):  
Hussin Che ◽  
Ahmad Ismail ◽  
Adem Kilicman ◽  
Amirah Azmi
Keyword(s):  
Approximate Analytical Solution ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Transform Method ◽  
Adomian Polynomials ◽  
Differential Transform ◽  
Non Linear ◽  
Klein Gordon ◽  
Time Region ◽  
Reduced Differential Transform Method

This paper explores the approximate analytical solution of non-linear Klein-Gordon equations (NKGE) by using multistep modified reduced differential transform method (MMRDTM). Through this proposed strategy, the non-linear term is substituted by associating Adomian polynomials obtained by utilization of a multistep approach. The NKGE solutions can be obtained with a reduced number of computed terms. In addition, the approximate solutions converge rapidly in a wide time region. Three examples are provided to illustrate the effectiveness of the proposed method to obtain solutions for the NKGE. Graphical results are shown to represent the behavior of the solution so as to demonstrate the validity and accuracy of the MMRDTM.

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