Introducing Undergraduate Students to Nonlinear Dynamics through A Numerical Approach

This paper describes a numerical method that used to solve the nonlinear Schr\"{o}dinger equation. The methods are an exponential time differencing method and a spectral method. The result indicates that at a certain parameter, fluctuation of wave function has contained chaotic dynamics. This case is expected to be used as an example for introducing numerical methods to undergraduate students on nonlinear dynamics. This introduction is deemed necessary, referring to the curriculum and syllabus used in several educational institutions in various countries that have included the topic of nonlinearity.