TITLE:
A Compact Finite Difference Schemes for Solving the Coupled Nonlinear Schrodinger-Boussinesq Equations
AUTHORS:
M. S. Ismail, H. A. Ashi
KEYWORDS:
Coupled Nonlinear Schrodinger-Boussinesq Equation, Conserved Quantities, Soliton, Plane Wave Solution, Fixed Point Method
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.7,
April
25,
2016
ABSTRACT: In this paper we are going to derive two numerical methods for
solving the coupled nonlinear Schrodinger-Boussinesq equation. The first method
is a nonlinear implicit scheme of second order accuracy in both directions time
and space; the scheme is unconditionally stable. The second scheme is a
nonlinear implicit scheme of second order accuracy in time and fourth order
accuracy in space direction. A generalized method is also derived where the
previous schemes can be obtained by some special values of l. The proposed methods will produced a
coupled nonlinear tridiagonal system which can be solved by fixed point method.
The exact solutions and the conserved quantities for two different tests are
used to display the robustness of the proposed schemes.