Error control in Adomian’s decomposition method applied to the time-dependent Gross-Pitaevskii equation. (English) Zbl 1115.65105
Summary: 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.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 35Q51 | Soliton equations |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
Keywords:
Gross-Pitaevskii equation; solitary wave solutions; numerical examples; error control; Adomian decomposition method; solitonsReferences:
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