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Computational and Mathematical Methods is an interdisciplinary journal dedicated to publishing the world's top research in the expanding area of computational mathematics, science and engineering.
Chief Editor, Professor Jesús Vigo Aguiar, is based at University of Salamanca, Spain. His core expertise is in mathematical applications.
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Employing a Modified Sumudu with a Modified Iteration Method to Solve the System of Nonlinear Partial Differential Equations
The Sumudu transform is presented in this paper in a modified form which is aimed at improving its performance and employing it along with a modified iteration method in order to determine the solution to a system of nonlinear partial differential equations. This includes a theoretical analysis of the associated modified Sumudu transform. It also includes an explanation of the mathematical method for utilizing the transform in conjunction with the modified iteration technique. The iteration method is employed to determine the nonlinear terms of the equations. The research is valuable in the sense that it allows approximate and exact solution configurations to be determined by combining the modified Sumudu transform with a modified iteration method. As another benefit, the modified Sumudu transform can be developed and enhanced to be applicable to a wide range of equations, making it an effective solution tool. By combining techniques, a final advantage is that the solutions can be derived quickly and easily as a result of the combined approach. Finally, an old transformation which has been modified from the Sumudu transform is combined with the modified iteration method to examine its capability of yielding convergent solutions by incorporating the modified iteration method into it.
A Fitted Numerical Approach for Singularly Perturbed Two-Parameter Parabolic Problem with Time Delay
This paper is aimed at constructing and analyzing a fitted approach for singularly perturbed time delay parabolic problems with two small parameters. The proposed computational scheme comprises the implicit Euler and especially finite difference method for the time and space variable discretization, respectively, on uniform step size. The stability and convergence analysis of the method is provided and is first-order parameter uniform convergent. Further, the numerical results depict that the present method is more convergent than some methods available in the literature.
Big Data Analytics for the ATLAS EventIndex Project with Apache Spark
The ATLAS EventIndex was designed to provide a global event catalogue and limited event-level metadata for ATLAS experiment of the Large Hadron Collider (LHC) and their analysis groups and users during Run 2 (2015-2018) and has been running in production since. The LHC Run 3, started in 2022, has seen increased data-taking and simulation production rates, with which the current infrastructure would still cope but may be stretched to its limits by the end of Run 3. A new core storage service is being developed in HBase/Phoenix, and there is work in progress to provide at least the same functionality as the current one for increased data ingestion and search rates and with increasing volumes of stored data. In addition, new tools are being developed for solving the needed access cases within the new storage. This paper describes a new tool using Spark and implemented in Scala for accessing the big data quantities of the EventIndex project stored in HBase/Phoenix. With this tool, we can offer data discovery capabilities at different granularities, providing Spark Dataframes that can be used or refined within the same framework. Data analytic cases of the EventIndex project are implemented, like the search for duplicates of events from the same or different datasets. An algorithm and implementation for the calculation of overlap matrices of events across different datasets are presented. Our approach can be used by other higher-level tools and users, to ease access to the data in a performant and standard way using Spark abstractions. The provided tools decouple data access from the actual data schema, which makes it convenient to hide complexity and possible changes on the backed storage.
A New Generated Family of Distributions: Statistical Properties and Applications with Real-Life Data
Several standard distributions can be used to model lifetime data. Nevertheless, a number of these datasets from diverse fields such as engineering, finance, the environment, biological sciences, and others may not fit the standard distributions. As a result, there is a need to develop new distributions that incorporate a high degree of skewness and kurtosis while improving the degree of goodness-of-fit in empirical distributions. In this study, by applying the T-X method, we proposed a new flexible generated family, the Ramos-Louzada Generator (RL-G) with some relevant statistical properties such as quantile function, raw moments, incomplete moments, measures of inequality, entropy, mean and median deviations, and the reliability parameter. The RL-G family has the ability to model “right,” “left,” and “symmetric” data as well as different shapes of the hazard function. The maximum likelihood estimation (MLE) method has been used to estimate the parameters of the RL-G. The asymptotic performance of the MLE is assessed by simulation analysis. Finally, the flexibility of the RL-G family is demonstrated through the application of three real complete datasets from rainfall, breaking stress of carbon fibers, and survival times of hypertension patients, and it is evident that the RL-Weibull, which is a special case of the RL-G family, outperformed its submodels and other distributions.
An Enhancement of the Accuracy of the BiCGStab Method for Solving Linear Systems with Single or Multiple Right-Hand Sides
In this paper, we present a technique to improve the convergence of the biconjugate gradient stabilized (BiCGStab) method. This method was developed by Van der Vorst for solving nonsymmetric linear systems with a single right-hand side. The global and block versions of the BiCGStab method have been proposed for solving nonsymmetric linear systems with multiple right-hand sides. Using orthogonal projectors to minimize the residual norm in each step, we get an enhancement of the convergence of each version of the BiCGStab method. The considered methods are BiCGStab, global BiCGStab, and block BiCGStab methods, noted, respectively, as Gl-BiCGStab and Bl-BiCGStab. To show the performance of our enhanced algorithms, we compare them with the standard, global, and block versions of the well-known generalized minimal residual method (GMRES).
Modeling of Angiogenesis in Tumor Blood Vessels via Lattice Boltzmann Method
This mathematical model studies the dynamics of tumor growth, one of the most complex dynamics problems that relates several interrelated processes over multiple ranges of spatial and temporal scales. In order to construct a tumor growth model, an angiogenesis model is used with focus on controlling the tumor volume, preventing new establishment, dissemination, and growth. The lattice Boltzmann method (LBM) is effectively applied to Navier-Stokes’ equation for obtaining the numerical simulation of blood flow through vasculature. It is observed that the flow features are extremely sensitive to stenosis severity, even at small strains and stresses, and that a severe effect on flow patterns and wall shear stresses is noticed in the tumor blood vessels. It is noted that based on the nonlinear deformation of the blood vessel’s wall, the flow rate conditions became unstable or distorted and affect the complex blood vessel’s geometry and it changes the blood flow pattern. When the blood flows inside the stenotic artery, depending on the presence of moderate or severe stenosis, it can lead to insufficient blood supply to the tissues in the downstream. Consequently, the highly disturbed flow occurs in the downstream of the stenosed artery, or even plaque ruptures happen when the flow pattern becomes very irregular and complex as it transits to turbulent which cannot be described without assumptions on the geometry. The results predicted by LBM-based code surpassed the expectations, and thus, the numerical results are found to be in great accord with the relevant established results of others.