Multivariate radial basis interpolation for solving quantum fluid dynamical equations

DOI10.1016/S0898-1221(01)00303-0zbMath0994.81027OpenAlexW2072659014MaRDI QIDQ1609118

Tak-San Ho, Xu-Guang Hu, Herschel Rabitz, Attila Askar

Publication date: 15 August 2002

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0898-1221(01)00303-0

zbMATH Keywords

Lagrangian descriptionBohmian mechanicsradial basis function interpolationsplit-operator method2D coherent state2D model of \(\text{NO}_2\) photodissociation dynamicsMadelung transformation

Mathematics Subject Classification ID

Software, source code, etc. for problems pertaining to quantum theory (81-04) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Coherent states (81R30) Foundations, quantum information and its processing, quantum axioms, and philosophy (81P99) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (2)

Radial basis function interpolation in the quantum trajectory method: optimization of the multi-quadric shape parameter. ⋮ High resolution finite volume scheme for the quantum hydrodynamic equations

Cites Work

• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• Stability analysis of finite difference schemes for quantum mechanical equations of motion
• Solution of the Schrödinger equation by a spectral method
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode
• Trajectory method for the time-dependent Schrödinger and Thomas-Fermi equations
• Unified theory of Lyapunov exponents and a positive example of deterministic quantum chaos
• On the approach to the stationary-state-scattering limit within Bohmian mechanics
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