We propose an Hermite spectral method for the Fokker-Planck-Landau (FPL) equation. Both distribution functions and collision terms are approximated by series expansions of functions. To handle complexity quadratic FPL operator, a reduced model is built adopting operator lower-order diffusive Fokker-Planck higher-order in expansion operator. The numerical scheme split into three steps according ...

We construct a fully-discrete finite element numerical scheme for the Cahn–Hilliard phase-field model of two-phase incompressible flow system with variable density and viscosity. The is linear, decoupled, unconditionally energy stable. Its key idea to combine penalty method Navier–Stokes equations Strang operator splitting method, introduce several nonlocal variables their ordinary differential...

Modern system dynamics is based upon a matrix representation of the dynamic equations governing the system behavior. A basic understanding of elementary matrix algebra is essential for the analysis of state-space formulated systems. A full discussion of linear algebra is beyond the scope of this note and only a brief summary is presented here. The reader is referred to a text on linear algebra,...

In their article on the cannabis debate, Strang et al raise the issue of cannabis and its effects on driving, suggesting that “a clearer understanding will be required of the extent to which a particular concentration of the drug (or its metabolites) can reliably be taken as evidence that an individual's driving ability was consequently impaired.” A review of the literature, however, suggests t...

A second-order accurate in time, positivity-preserving, and unconditionally energy stable operator splitting scheme is proposed analyzed for reaction-diffusion systems with the detailed balance condition. The designed based on an energetic variational formulation, which reaction part reformulated terms of trajectory, both diffusion parts dissipate same free energy. At stage, trajectory equation...

In the present manuscript, Benjamin-Bona-Mahony-Burgers (BBMB) equation will be handled numerically by Strang time-splitting technique. While applying this technique, collocation method based on quintic B-spline basis functions is applied. line with our purpose, after splitting BBM-Burgers given appropriate initial boundary conditions into two subequations containing derivative in terms of time...

Y. Nakamura and H. Hanafusa, “Inverse kinematic solutions with singularity robustness for robot manipulator control,” ASME J. Dynam. Sysr., Meas., Conrr., vol. 108, pp. 163-171, Sept. 1986. C. W. Wampler II, “Manipulator inverse kinematic solutions based on vector formulations and damped least-squares method,” IEEE Trans. Sysf. Man Cybem., vol. SMC-16, no. 1, pp. 93-101, Jan./Feb. 1986. A. A. M...