RT info:eu-repo/semantics/article
T1 CMMSE: analysis and comparison of some numerical methods to solve a nonlinear fractional Gross–Pitaevskii system
A1 Serna-Reyes, Adán
A1 Macías Díaz, Jorge E.
A1 Gallegos, Armando
A1 Reguera López, Nuria
K1 Fractional Bose–Einstein model
K1 Double-fractional system
K1 Fully discrete model
K1 Stability and convergence analysis
K1 Matemáticas
K1 Mathematics
AB In this work, we introduce and theoretically analyze various computational techniques to approximate the solutions of solve a fractional extension of a double condensate system. More precisely, the continuous model extends the well-known Gross–Pitaevskii equation to the fractional scenario, and considering two interacting condensates. The mathematical system considers two complex-valued regimes with coupling, and a mass and energy functions are associated to this model. Both are constant in time. Here, various discretizations are analyzed to solve this system. Some of them are able to preserve the mass and the energy, some are not. We discuss the existence of solutions, the consistency of the models, the stability and the convergence. Finally, from the computational point of view, some algorithms are simpler to code than others. In fact, those for which the mass and the energy are conserved are more difficult to implement. We discuss here pros and cons.
PB Springer
SN 0259-9791
YR 2022
FD 2022-08
LK http://hdl.handle.net/10259/8076
UL http://hdl.handle.net/10259/8076
LA eng
NO One of us (J.E.M.-D.) wishes to acknowledge the financial support from the National Council for Science and Technology of Mexico (CONACYT) through Grant A1-S-45928.
DS Repositorio Institucional de la Universidad de Burgos
RD 09-may-2024