Computational and Mathematical Methods最新文献

{"title":"Employing a Modified Sumudu with a Modified Iteration Method to Solve the System of Nonlinear Partial Differential Equations","authors":"Junaid Idrees Mustafa","doi":"10.1155/2023/6649037","DOIUrl":"https://doi.org/10.1155/2023/6649037","url":null,"abstract":"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.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"66 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135093349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Fitted Numerical Approach for Singularly Perturbed Two-Parameter Parabolic Problem with Time Delay","authors":"Imiru Takele Daba, Wondwosen Gebeyaw Melesse, Guta Demisu Kebede","doi":"10.1155/2023/6496354","DOIUrl":"https://doi.org/10.1155/2023/6496354","url":null,"abstract":"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.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"17 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134973783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Big Data Analytics for the ATLAS EventIndex Project with Apache Spark","authors":"Álvaro Fernández Casaní, Carlos García Montoro, Santiago González de la Hoz, José Salt, Javier Sánchez, Miguel Villaplana Pérez","doi":"10.1155/2023/6900908","DOIUrl":"https://doi.org/10.1155/2023/6900908","url":null,"abstract":"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.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135536157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A New Generated Family of Distributions: Statistical Properties and Applications with Real-Life Data","authors":"John Kwadey Okutu, Nana K. Frempong, Simon K. Appiah, Atinuke O. Adebanji","doi":"10.1155/2023/9325679","DOIUrl":"https://doi.org/10.1155/2023/9325679","url":null,"abstract":"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.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135059442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Enhancement of the Accuracy of the BiCGStab Method for Solving Linear Systems with Single or Multiple Right-Hand Sides","authors":"F. Bouyghf","doi":"10.1155/2023/8078760","DOIUrl":"https://doi.org/10.1155/2023/8078760","url":null,"abstract":"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).","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135734361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A novel two-parameter class of optimized hybrid block methods for integrating differential systems numerically","authors":"Gurjinder Singh,&nbsp;Arvind Garg,&nbsp;Rajat Singla,&nbsp;Vinay Kanwar","doi":"10.1002/cmm4.1214","DOIUrl":"10.1002/cmm4.1214","url":null,"abstract":"<p>In this article, a two-parameter class of hybrid block methods for integrating first-order initial value ordinary differential systems is proposed. The methods exhibit hybrid nature which helps in bypassing the first Dahlquist barrier existing for linear multistep methods. The approach used in the development of a class of methods is purely interpolation and collocation technique. The class of methods is based on four intra-step points from which two intra-step points have been optimized by using an optimization strategy. In this optimization strategy, the values of two intra-step points are obtained by minimizing the local truncation errors of the formulas at the points <math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math> and <math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math>.The order of accuracy of the proposed methods is six. A method as a special case of this class of methods is considered and developed into a block form which produces approximate numerical solutions at several points simultaneously. Further, the method is formulated into an adaptive step-size algorithm using an embedded type procedure. This method which is a special case of this class of methods has been tested on six well-known first-order differential systems.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1214","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91332636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A collection of efficient tools to work with almost strictly sign regular matrices","authors":"Pedro Alonso Velázquez,&nbsp;Jorge Jiménez Meana,&nbsp;Juan Manuel Peña Ferrández,&nbsp;María Luisa Serrano Ortega","doi":"10.1002/cmm4.1212","DOIUrl":"10.1002/cmm4.1212","url":null,"abstract":"<p>In this work, several algorithms have been implemented with Matlab to obtain an algorithmic characterizations of almost strictly sign regular matrices using Neville elimination.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1212","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90819506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The change of the Weierstrass structure under one row perturbation","authors":"Itziar Baragaña,&nbsp;Alicia Roca","doi":"10.1002/cmm4.1211","DOIUrl":"10.1002/cmm4.1211","url":null,"abstract":"<p>In this work we study the change of the structure of a regular pencil when we perform small perturbations over some of its rows and the other rows remain unaltered. We provide necessary conditions when several rows are perturbed, and prove them to be sufficient to prescribe the homogenous invariant factors or the Weyr characteristic of the resulting pencil when one row is perturbed.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1211","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87421869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hybrid method for two parameter singularly perturbed elliptic boundary value problems","authors":"Anuradha Jha,&nbsp;Mohan Krishen Kadalbajoo","doi":"10.1002/cmm4.1210","DOIUrl":"10.1002/cmm4.1210","url":null,"abstract":"<p>In this article, a hybrid scheme for a two-parameter elliptic problem with regular exponential and boundary layers on Shishkin mesh is analyzed. The hybrid scheme comprises the central difference method in the layer region and the upwind method in the regular part. The use of the central difference in layer region results in a more accurate resolution of layers. The method is shown to have first-order parameter uniform convergence. The numerical results corroborate the error estimates presented here.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1210","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86916121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new family of \u0000 \u0000 𝒜\u0000 −\u0000 acceptable nonlinear methods with fixed and variable stepsize approach","authors":"Sania Qureshi,&nbsp;Amanullah Soomro,&nbsp;Evren Hınçal","doi":"10.1002/cmm4.1213","DOIUrl":"10.1002/cmm4.1213","url":null,"abstract":"<p>Solving stiff, singular, and singularly perturbed initial value problems (IVPs) has always been challenging for researchers working in different fields of science and engineering. In this research work, an attempt is made to devise a family of nonlinear methods among which second- to fourth-order methods are not only <math>\u0000 <mrow>\u0000 <mi>𝒜</mi>\u0000 <mo>−</mo>\u0000 </mrow></math> stable but <math>\u0000 <mrow>\u0000 <mi>𝒜</mi>\u0000 <mo>−</mo>\u0000 </mrow></math> acceptable as well under order stars' conditions. These features make them more suitable for solving stiff and singular systems in ordinary differential equations. Methods with remaining orders are either zero- or conditionally stable. The theoretical analysis contains local truncation error, consistency, and order of accuracy of the proposed nonlinear methods. Furthermore, both fixed and variable stepsize approaches are introduced wherein the latter improves the performance of the devised methods. The applicability of the methods for solving the system of IVPs is also described. When used to solve problems from physical and real-life applications, including nonlinear logistic growth and stiff model for flame propagation, the proposed methods are found to have good results.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1213","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88922027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}