Numerical investigation of the solutions of Schrodinger equation with exponential cubic B-spline finite element method
For researchers in computational physics, this is an incremental improvement over existing B-spline methods for solving nonlinear Schrödinger equations.
The paper applies an exponential cubic B-spline finite element method to solve the cubic nonlinear Schrödinger equation, demonstrating accuracy and efficiency through four test problems including soliton dynamics.
In this paper, we investigate the numerical solutions of the cubic nonlinear Schrodinger equation via the exponential B-spline collocation method. Crank-Nicolson formulas are used for time discretization of the target equation. A linearization technique is also employed for the numerical purpose. Four numerical examples related to single soliton, collision of two solitons that move in opposite directions, the birht of standing and mobile solitons and bound state solution are considered as the test problems. The accuracy and the efficiency of the purposed method are measured by max error norm and conserved constants. The obtained results are compared with the possible analytical values and those in some earlier studies.