Numerical simulation of one-dimensional nonlinear Schrodinger equation using PSO with exponential B-spline

Abstract

Particle swarm optimization (PSO) is a widely adopted, rapid, efficient, and computer-friendly technique for optimization in various fields, including computer science, engineering, and mathematical modelling. In this paper, the nonlinear Schrodinger (NLS) equation has been solved numerically, which leads to soliton-type solutions, by utilizing the “Exponential cubic B-spline differential quadrature method (Expo-MCB-DQM) with PSO”. The exponential cubic B-spline basis functions involve a parameter that must be assigned a value to find the numerical solutions. Until now, the value of a parameter had been determined by the hit-and-trial approach, which leads to unstable results. By employing the PSO technique, the optimal value of the parameter is determined, which enhances the accuracy of the numerical solutions. This study introduces an innovative combination of Expo-MCB-DQM with PSO, which is an innovative combination that optimizes the parameters in the basis function, leading to improved outcomes. To validate the authenticity and effectiveness of this methodology, it has been applied to two problems to present the numerical results in comparison with the exact solution. Additionally, the paper provides insightful discussions on the significant application of the NLS equation in optical fiber communication.

Keywords

• Differential quadrature method
• Exponential cubic B-spline
• Particle swarm optimization
• Nonlinear Schrodinger equation: optical fiber communication