This study used the reinforcing spirals model to investigate the mutual influence between individuals’ media use and their global warming perceptions. Data from the science module of the 2006 General Social Survey were analyzed using structural equation modeling. Results offered support for the reinforcing spirals model’s predictions. Media use mediated the effects of age, race, and education o...

In this article we consider iterative operator-splitting methods for nonlinear differential equations. The main feature of the proposed idea is the embedding of Newton’s method for solving the split parts of the nonlinear equation at each step. The convergence properties of such a mixed method are studied and demonstrated. We confirm with numerical applications the effectiveness of the proposed...

Many applied time-dependent problems are characterized by an additive representation of the problem operator. Additive schemes are constructed using such a splitting and associated with the transition to a new time level on the basis of the solution of more simple problems for the individual operators in the additive decomposition. We consider a new class of additive schemes for problems with a...

The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector φ1 of ...

We consider a prototype two-phase uid-ow model with capillary forces. The pressure equation is solved using standard nite-elements and multigrid techniques. The parabolic saturation equation is addressed via a novel corrected operator splitting approach. In typical applications, the importance of advection versus diiusion (capillary forces) may change rapidly during a simulation. The corrected ...

Contents Introduction 5 Chapter 1. The theory in the smooth framework 11 1.1. The ordinary differential equation 11 1.2. Existence and uniqueness in the classical setting 11 1.3. The classical flow of a vector field 16 1.4. The transport equation and the continuity equation 19 Part 1. The Eulerian viewpoint 23 Chapter 2. Renormalized solutions and well-posedness of the PDE 25 2.1. A strategy to...

Approximate solutions of the Fisher equation obtained by different splitting methods are investigated. The error of this nonlinear problem is analyzed. The order of different splitting methods coupled with numerical methods of different order is calculated numerically and symbolically.