Gurjinder Singh, Arvind Garg, Rajat Singla, Vinay Kanwar
{"title":"A novel two-parameter class of optimized hybrid block methods for integrating differential systems numerically","authors":"Gurjinder Singh, Arvind Garg, Rajat Singla, 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}
Pedro Alonso Velázquez, Jorge Jiménez Meana, Juan Manuel Peña Ferrández, María Luisa Serrano Ortega
{"title":"A collection of efficient tools to work with almost strictly sign regular matrices","authors":"Pedro Alonso Velázquez, Jorge Jiménez Meana, Juan Manuel Peña Ferrández, 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, 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, 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, Amanullah Soomro, 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}