in this paper, we investigate the total variation diminishing property for a class of 2-stage explicit rung-kutta methods of order two (rk2) when applied to the numerical solution of special nonlinear initial value problems (ivps) for (odes). schemes preserving the essential physical property of diminishing total variation are of great importance in practice. such schemes are free of spurious o...

In the object oriented literature the notion of a variation point is important. A variation point is where we expect to, or, in retrospect, are forced to, accommodate alternative solutions. Numerical software, such as solvers for partial differential equations (PDEs), are full of variation points. We observe this from how we speak about PDEs. Firstly, we speak about a multitude of PDEs to descr...

There has been significant progress in our understanding of Free Choice any and of -ever free relatives in recent years. Very often, however, the investigation of these two Free Choice Items (FCI) in English has been conducted in parallel. One of the aims of this paper is to bring the two strands together in a way that can account for commonalities and differences between them and, perhaps, a t...

In this article, small scale effects on free vibration analysis of non-uniform nanobeams is discussed. Small scale effects are modelled after Eringen’s nonlocal elasticity theory while the non-uniformity is presented by exponentially varying width among the beams length with constant thickness. Analytical solution is achieved for free vibration with different boundary conditions. It is shown th...

Instabilities of a thin viscous film flowing down a uniformly heated plane are investigated in this study. The heating generates a surface tension gradient that induces thermocapillary stresses on the free surface. Thus, the film is not only influenced by gravity and mean surface tension but also the thermocapillary force is acting on the free surface. Moreover, the heat transfer at the free su...