Abstract
In this paper, we derive numerical methods for solving the coupled nonlinear Schrödinger equation. We discretize the space derivative by central difference formulas of fourth-order. The resulting ordinary differential system is solved by the fourth-order explicit Runge–Kutta method. Neumann and Periodic boundary conditions are used. The method is tested for accuracy and the conserved quantities. These methods conserve the three conserved quantities conserve exactly for at least five decimal places. A comparison has been made with some existing methods.