Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain

Abstract

We present a class of orthogonal functions on infinite domain based on Jacobi polynomials. These functions are generated by applying a tanh transformation to Jacobi polynomials. We construct interpolation and projection error estimates using weighted pseudo‐derivatives tailored to the involved mapping. Then, using the nodes of the newly introduced tanh Jacobi functions, we develop an efficient spectral tanh Jacobi collocation method for the numerical simulation of nonlinear Schrödinger equations on the infinite domain without using artificial boundary conditions. The applicability and accuracy of the solution method are demonstrated by two numerical examples for solving the nonlinear Schrödinger equation and the nonlinear Ginzburg–Landau equation.