scholarly journals Numerical computation of successive approximations method and variational iteration method for solving Klein-Gordon Schrödinger equation

2021 ◽  
Keyword(s):  
Schrödinger Equation ◽  
Numerical Computation ◽  
Iteration Method ◽  
Schrodinger Equation ◽  
Variational Iteration Method ◽  
Successive Approximations ◽  
Variational Iteration ◽  
Klein Gordon

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 Fractional Variational Iteration Method and Its Application to Fractional Partial Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Iteration Method ◽  
Fractional Derivatives ◽  
Financial Models ◽  
Gordon Equation ◽  
Burgers Equation ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Liouville Derivative ◽  
Black Scholes ◽  
Klein Gordon

We use the fractional variational iteration method (FVIM) with modified Riemann-Liouville derivative to solve some equations in fluid mechanics and in financial models. The fractional derivatives are described in Riemann-Liouville sense. To show the efficiency of the considered method, some examples that include the fractional Klein-Gordon equation, fractional Burgers equation, and fractional Black-Scholes equation are investigated.

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