This paper examines the stability and convergence of discretisa-tions of initial value p.d.e.'s using spatial discretisation followed by time integration with an explicit one-step method. A Cauchy integral representation is used to bound the growth in the discrete solution. New results are obtained regarding suucient conditions for both algebraic and strong stability. Suucient conditions are al...

In this study, we analyze the development experience of eco-tourism in different regions of china to find the common regional convergence which is checked with ADF test and co-integration relations. In our results, we could contribute as theoretical foundation for regional development of ecotourism in China. Meanwhile, the research result of convergence of regional eco-agricultural tourism in C...

This content-centric view misses the real digital convergence. When viewed from a socio-anthropological standpoint, the more profound convergence is that of content, context, and collaboration, which will result in the integration of individuals and their society, processes, goals and content into on-line communities. Members are typically exposed to a greater range of ideas, viewpoints and too...

A criterion is established for the convergence of sequences of a general type of Runge-Kutta method. The criterion is expressed in terms of "weak convergence", a property defined in the paper.

Quasi-Monte Carlo methods are based on the idea that random Monte Carlo techniques can often be improved by replacing the underlying source of random numbers with a more uniformly distributed deterministic sequence. Quasi-Monte Carlo methods often include standard approaches of variance reduction, although such techniques do not necessarily directly translate. In this paper we present a quasi-M...

In this paper we study multivariate integration for a weighted Korobov space for which the Fourier coefficients of the functions decay exponentially fast. This implies that the functions of this space are infinitely times differentiable. Weights of the Korobov space monitor the influence of each variable and each group of variables. We show that there are numerical integration rules which achie...

Advanced process technology and system-integration provide the driving forces behind silicon convergence. FPGAs speed along this trajectory, having already integrated SRAM memories, digital signal processing (DSP) and multiplier blocks, serial transceivers, memory controllers, and advanced I/O functions. The latest advancement in programmable technology is the SoC, which integrates an Altera® F...

Since the solution of a second-kind Volterra integral equation with weakly singular kernel has, in general, unbounded derivatives at the left endpoint of the interval of integration, its numerical solution by polynomial spline collocation on uniform meshes will lead to poor convergence rates. In this paper we investigate the convergence rates with respect to graded meshes, and we discuss the pr...

A staggered Runge-Kutta (staggered RK) scheme is the time integration Runge-Kutta type scheme based on staggered grid, which was proposed by Ghrist and Fornberg and Driscoll in 2000. Afterwords, Vewer presented efficiency of the scheme for linear and semilinear wave equations through numerical experiments. We study stability and convergence properties of this scheme for semilinear wave equation...

Industry convergence is the future trend of industrial development in rural areas and conducive to high-quality agriculture development. To explore dynamics industry convergence. This paper selects data from 31 provincial administrative regions China 2009 2019. It uses entropy power method measure quality integration empirically studies impact transportation infrastructure on using a spatial pa...