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Sarker, P. and Chakravarty, U.K. (2020) A Generalization of the Method of Lines for the Numerical Solution of Coupled, Forced Vibration of Beams. Mathematics and Computers in Simulation, 170, 115-142.
https://doi.org/10.1016/j.matcom.2019.10.011

has been cited by the following article:

• TITLE: Method of Lines for the Chiral Nonlinear Schrödinger Equation

  AUTHORS: K. S. AL-Basyouni, M. S. Ismail

  KEYWORDS: Method of Lines, Linear Multistep Method, Chiral Soliton, Interaction of Two Solitons

  JOURNAL NAME: Applied Mathematics, Vol.11 No.6, June 3, 2020

  ABSTRACT: In this paper, we solve chiral nonlinear Schrodinger equation (CNSE) numerically. Two numerical methods are derived using the explicit Runge-Kutta method of order four and the linear multistep method (Predictor-Corrector method of fourth order). The resulting schemes of fourth order accuracy in spatial and temporal directions. The CNSE is non-integrable and has two kinds of soliton solutions: bright and dark soliton. The exact solutions and the conserved quantities of CNSE are used to display the efficiency and robustness of the numerical methods we derived. Interaction of two bright solitons for different parameters is also displayed.