Stationary Solution of a Time Dependent Density Matrix Formalism

Convergence of Time-Dependent Turing Structures to a Stationary Solution

Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written for the L norm of the solution. This method is appropriate for the equations with time dependent coefficients. It yields new results and is applicable when the...

ON THE STATIONARY PROBABILITY DENSITY FUNCTION OF BILINEAR TIME SERIES MODELS: A NUMERICAL APPROACH

In this paper, we show that the Chapman-Kolmogorov formula could be used as a recursive formula for computing the m-step-ahead conditional density of a Markov bilinear model. The stationary marginal probability density function of the model may be approximated by the m-step-ahead conditional density for sufficiently large m.

Localized-density-matrix implementation of time-dependent density-functional theory

Density matrix based time-dependent density functional theory and the solution of its linear response in real time domain.

A density matrix based time-dependent density functional theory is extended in the present work. Chebyshev expansion is introduced to propagate the linear response of the reduced single-electron density matrix upon the application of a time-domain delta-type external potential. The Chebyshev expansion method is more efficient and accurate than the previous fourth-order Runge-Kutta method and re...

Numerical solution of time-dependent foam drainage equation (FDE)

Reduced Differental Transform Method (RDTM), which is one of the useful and effective numerical method, is applied to solve nonlinear time-dependent Foam Drainage Equation (FDE) with different initial conditions. We compare our method with the famous Adomian Decomposition and Laplace Decomposition Methods. The obtained results demonstrated that RDTM is a powerful tool for solving nonlinear part...