We present a fast and accurate numerical scheme for the approximation of the primitive equations of the atmosphere. The temporal variable is discretized by using a special semiimplicit scheme which requires only to solve a Helmholtz equation and a nonlocal Stokes problem at each time step; the spatial variables are discretized by a spectral-Galerkin procedure with the horizontal components of v...

A Fortran IV computer program is documented, implementing a Galerkin finite-element method for solving the non-linear shallow-water equations on a limited domain. The resulting ordinary differential equations are integrated using a finite-difference discretization method in time. A time-extrapolated Crank-Nicolson numerical integration scheme is employed to quasi-linearize the non-linear advect...

in this work, based on experimental observations and exact theoretical predictions, the kinetic scheme of raft polymerization is extended to a wider range of reactions such as irreversible intermediate radical terminations and reversible transfer reactions. the reactions which have been labeled as kinetic scheme are the more probable existing reactions as the theoretical point of view. the deta...

In this article, we construct a fully discrete finite element numerical scheme with linearity, decoupling, unconditional energy stability, and second-order time accuracy for the Navier-Stokes coupled phase-field crystal model. The key idea is based on design of several auxiliary ODEs, combined method spatial discretization, projection equations, IEQ type nonlinear potentials. At each step, by u...

Random numbers are arranged in a circle. At each time step, the lowest number, and the numbers at its two neighbors, are each replaced by new random numbers. That’s all! This step is repeated again and again. What could be simpler than replacing some random numbers with some other random numbers? Who says that complexity cannot be simple? This simple scheme leads to rich behavior beyond what we...

We propose a fully distributed Newton-type algorithm for state estimation of electric power systems. At each Newton iteration, matrix-splitting techniques are utilized to carry out the matrix inversion for calculating the Newton step in a distributed fashion. In order to reduce the communication burden as well as increase robustness of state estimation, the proposed distributed scheme relies on...