Multivariate radial basis interpolation for solving quantum fluid dynamical equations

This paper proposes a new numerical technique for solving the quantum fluid dynamical equations within the Lagrangian description. An efficient and accurate numerical scheme is achieved by taking advantage of the smooth field variables obtained via the Madelung transformation combined with the radial basis function interpolation. Applications to the 2D coherent state and a 2D model of NO₂ photodissociation dynamics show that the present method rivals the split-operator method in both efficiency and accuracy. The advantage of the new algorithm as a computational tool is expected to prevail for high-dimensional systems.