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Technical Brief

The Time-Splitting Spectral Method for the Gerdjikov-Ivanov Equation with the Riesz Fractional Derivative in the Quantum Field Theory

[+] Author and Article Information
Santanu Saha Ray

National Institute of Technology, Department of Mathematics, Rourkela-769008, India
santanusaharay@yahoo.com

1Corresponding author.

ASME doi:10.1115/1.4041891 History: Received May 05, 2018; Revised October 24, 2018

Abstract

The present work deals with the solutions of the Gerdjikov-Ivanov(G-I) equation with the Riesz fractional derivative by means of the time splitting spectral approach. In this approach the G-I equation is split into two equations and the proposed technique viz. time splitting spectral method is employed for discretizing the equation in space and then subsequently integrating in time exactly. Furthermore, an implicit finite difference method is utilized here to compare the results with the above semi-numerical method viz. time-splitting spectral technique. Moreover it has been established that the proposed method is unconditionally stable. In addition to these, the error norms have been also presented here.

Copyright (c) 2018 by ASME
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