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Unconditional convergence of linearized implicit finite difference method for the 2D/3D Gross-Pitaevskii equation with angular momentum rotation
- Source :
- Science China Mathematics. 62:1669-1686
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
Abstract
- This paper is concerned with the time-step condition of linearized implicit finite difference method for solving the Gross-Pitaevskii equation with an angular momentum rotation term. Unlike the existing studies in the literature, where the cut-off function technique was used to establish the error estimates under some conditions of the time-step size, this paper introduces an induction argument and a ‘lifting’ technique as well as some useful inequalities to build the optimal maximum error estimate without any constraints on the time-step size. The analysis method can be directly extended to the general nonlinear Schrodinger-type equations in twoand three-dimensions and other linear implicit finite difference schemes. As a by-product, this paper defines a new type of energy functional of the grid functions by using a recursive relation to prove that the proposed scheme preserves well the total mass and energy in the discrete sense. Several numerical results are reported to verify the error estimates and conservation laws.
- Subjects :
- Conservation law
Angular momentum
General Mathematics
Finite difference
Finite difference method
010103 numerical & computational mathematics
Function (mathematics)
01 natural sciences
010101 applied mathematics
Nonlinear system
Applied mathematics
Unconditional convergence
0101 mathematics
Energy functional
Mathematics
Subjects
Details
- ISSN :
- 18691862 and 16747283
- Volume :
- 62
- Database :
- OpenAIRE
- Journal :
- Science China Mathematics
- Accession number :
- edsair.doi...........2b5cf394e467f2b6ec112e050b65c797