The smoothed particle hydrodynamics method for solving generalized variable coefficient Schrodinger equation and SchrodingerBoussinesq system

A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic elds. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary di erential equations (ODEs). Also, in the numerical methods for solving the time-dependent PDEs, based on the meshless methods, to achieve acceptable results, the temporal direction must be discretized using an e ective technique. Thus, in the current paper, we apply the fourth-order exponential time di erenceing Runge-Kutta method (ETDRK4) for the obtained system of ODEs. The aim of this paper is to show that the meshless method based on the generalized SPH approach is suitable for the treatment of the nonlinear complex partial di erential equations. Numerical examples con rm the efficiency of proposed scheme