The approximate solution of the problem of controlling an initial value problem for a linear system of autonomous ordinary differential equations is considered. The corresponding homogeneous solution to the differential equation is assumed to be non-expansive and the inhomogeneity is a linear function of the control variable that is constant along a priori given sub-intervals. The optimal contr...

Boltzmann Transport Equation is solved numerically to model phonon transport in a subcontinuum domain in order to study heat transfer in thin film semiconductors. The phonon distribution function is modified to get an Energy equation from the Boltzmann Transport Equation. Gray form of the Energy equation is solved in the Relaxation time approximation to get the Phonon Energy Density distributio...

In this paper, we present a time splitting scheme for the Schrödinger equation in the presence of electromagnetic eld in the semi-classical regime, where the wave function propagates O(ε) oscillations in space and time. With the operator splitting technique, the time evolution of the Schrödinger equation is divided into three parts: the kinetic step, the convection step and the potential step. ...

We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our analysis is conducted by first casting the domain decomposition procedure into a variational framework based on weighted Sobolev spaces. The time integration of a...

Fey’s Method of Transport (MoT ) is a multidimensional flux-vector-splitting scheme for systems of conservation laws. Similarly to its one-dimensional forerunner, the Steger–Warming scheme, and several other upwind finite-difference schemes, the MoT suffers from an inconsistency at sonic points when used with piecewise-constant reconstructions. This inconsistency is due to a cell-centered evolu...

Because of the global warming and the rising sea level, residents living in southwestern coastland, Taiwan are faced with the submerged land and may move to higher elevation area. It is desirable to discuss the key consideration factor for selecting the migration location under five dimensions of security”, “health”, “convenience”, “comfort” and “socio-economic” based on the document reviews. T...

Stratospheric sudden warmings are the clearest and strongest manifestation of dynamical coupling in the stratosphere–troposphere system. While many sudden warmings have been individually documented in the literature, this study aims at constructing a comprehensive climatology: all major midwinter warming events are identified and classified, in both the NCEP–NCAR and 40-yr ECMWF Re-Analysis (ER...

Operator splitting is a numerical method of computing the solution to a differential equation. The splitting method separates the original equation into two parts over a time step, separately computes the solution to each part, and then combines the two separate solutions to form a solution to the original equation. A canonical example is splitting of diffusion terms and convection terms in a c...