Name
Abstract | ||
|---|---|---|
The phase flow method, originally introduced in [L. X. Ying and E. J. Candés, J. Comput. Phys., 220 (2006), pp. 184-215], can efficiently solve autonomous ordinary differential equations. In [S. Jin, H. Wu, and Z. Y. Huang, SIAM J. Sci. Comput., 31 (2008), pp. 1303-1321], the method was generalized to solve Hamiltonian system where the Hamiltonian function was discontinuous. However, both of these methods require a phase flow map constructed on an invariant manifold. This can increase computational cost when the invariant domain is big or unbounded. Following the idea of [S. Jin, H. Wu, and Z. Y. Huang, SIAM J. Sci. Comput., 31 (2008), pp. 1303-1321], we propose a hybrid phase flow method for solving the Liouville equation in a bounded domain, which is smaller than the invariant manifold of a phase flow map. By using some proper boundary conditions, this method can help solve the problem where the invariant manifold of a phase flow map determined by the Liouville equation is unbounded. We verify numerical accuracy and efficiency by several examples of the semiclassical limit of the Schrödinger equation. Analysis of numerical stability and convergence is given for the semiclassical limit equation with inflow boundary condition. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1137/090773726 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
bounded domain,liouville equation,h. wu,hybrid phase flow method,s. jin,flow method,phase flow method,siam j. sci,phase flow map,phase flow,invariant manifold,hybrid phase,z. y. huang,hamiltonian system | Boundary value problem,Mathematical optimization,Ordinary differential equation,Mathematical analysis,Schrödinger equation,Hamiltonian system,Hamiltonian mechanics,Invariant (mathematics),Invariant manifold,Numerical stability,Mathematics | Journal |
Volume | Issue | ISSN |
49 | 2 | 0036-1429 |
Citations | PageRank | References |
1 | 0.37 | 5 |
Authors | ||
2 | ||