A new perspective to get numerical solution of one and two dimensional coupled non-linear Schrodinger equation by implementing differential quadrature method using hyperbolic B-spline

Abstract

In this research work, we represent a novel technique named Hyperbolic B -spline based Differential quadrature method to get the numerical approximations of the 1D and 2D coupled non-linear Schrodinger equation. The coupled non-linear Schrodinger equation represents the range of physical phenomena with the aid of a model equation for the optical fiber with the linear birefringence. In present paper, Differential quadrature method is applied over the mentioned PDE and reduced set of ordinary differential equations is solved by SSP-RK43 scheme. Accuracy and effectiveness of the proposed scheme is checked by $L_\infty$ error norm and conservation of mass property is also tested. In present paper, elastic property is also checked, whether the wave amplitudes have restored their shapes or not for the different used parameters and stability of the proposed scheme is checked via matrix stability analysis method, which indicates that the present method has the property of unconditionally stable.