An Analysis of the Robust Convergent Method for a Singularly Perturbed Linear System of Reaction–Diffusion Type Having Nonsmooth Data

In this paper, a coupled system of [Formula: see text] second-order singularly perturbed differential equations of reaction–diffusion type with discontinuous source term subject to Dirichlet boundary conditions is studied, where the diffusive term of each equation is being multiplied by the small perturbation parameters having different magnitudes and coupled through their reactive term. A discontinuity in the source term causes the appearance of interior layers on either side of the point of discontinuity in the continuous solution in addition to the boundary layer at the end points of the domain. Unlike the case of a single equation, the considered system does not obey the maximum principle. To construct a numerical method, a classical finite difference scheme is defined in conjunction with a piecewise-uniform Shishkin mesh and a graded Bakhvalov mesh. Based on Green’s function theory, it has been proved that the proposed numerical scheme leads to an almost second-order parameter-uniform convergence for the Shishkin mesh and second-order parameter-uniform convergence for the Bakhvalov mesh. Numerical experiments are presented to illustrate the theoretical findings. </jats:p

Identifying Requirements for Big Data Analytics and Mapping to Hadoop Tools

Big data is being generating in a wide variety of formats at an exponential rate. Big data analytics deals with processing and analyzing voluminous data to provide useful insight for guided decision making. The traditional data storage and management tools are not well-equipped to handle big data and its application. Apache Hadoop is a popular open-source platform that supports storage and processing of extremely large datasets. For the purposes of big data analytics, Hadoop ecosystem provides a variety of tools. However, there is a need to select a tool that is best suited for a specific requirement of big data analytics. The tools have their own advantages and drawbacks over each other. Some of them have overlapping business use cases however they differ in critical functional areas. So, there is a need to consider the trade-offs between usability and suitability while selecting a tool from Hadoop ecosystem. This paper identifies the requirements for Big Data Analytics (BDA) and maps tools of the Hadoop framework that are best suited for them. For this, we have categorized Hadoop tools according to their functionality and usage. Different Hadoop tools are discussed from the users’ perspective along with their pros and cons, if any. Also, for each identified category, comparison of Hadoop tools based on important parameters is presented. The tools have been thoroughly studied and analyzed based on their suitability for the different requirements of big data analytics. A mapping of big data analytics requirements to the Hadoop tools has been established for use by the data analysts and predictive modelers.</jats:p