Error control in Adomian's decomposition method applied to the time-dependent Gross–Pitaevskii equation

Abstract

We apply the Adomian decomposition method to the one-dimensional time-dependent Gross–Pitaevskii equation, which describes the evolution of bright solitons. We investigate the behaviour of the error in the solutions obtained by the Adominan method and make a comparison with the exact solution. We obtain a formula for the error as a function of time and the number of Adomian polynomials used.

Keywords:

• Gross–Pitaevskii equation
• Solitary wave solutions
• Numerical methods