Taylor Collocation Method for the Numerical Solution of the Nonlinear Schrodinger Equation Using Quintic B-Spline Basis

摘要

In this study, we construct a Taylor collocation method for the numerical solution of the nonlinear Schrodinger (NLS) equation. We use suitable initial and boundary conditions. Taylor series expansion is used for time discretization. The cubic B-spline collocation method is applied to spatial discretization. Test problems concerning the single soliton motion, interaction of two colliding solitons, and the formation and bound states of solitons of the NLS equation are studied to evaluate the method. The L_2 and L_∞ error norms are calculated to improve the accuracy of the numerical results.