{"title":"Numerical Methods for Fractional Differentiation","authors":"K. M. Owolabi, A. Atangana","doi":"10.1007/978-981-15-0098-5","DOIUrl":"https://doi.org/10.1007/978-981-15-0098-5","url":null,"abstract":"","PeriodicalId":176863,"journal":{"name":"Springer Series in Computational Mathematics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130957317","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":"Tensor Spaces and Numerical Tensor Calculus","authors":"W. Hackbusch","doi":"10.1007/978-3-642-28027-6","DOIUrl":"https://doi.org/10.1007/978-3-642-28027-6","url":null,"abstract":"","PeriodicalId":176863,"journal":{"name":"Springer Series in Computational Mathematics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128150183","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":"Mixed and Hybrid Finite Element Methods","authors":"F. Brezzi, M. Fortin","doi":"10.1007/978-1-4612-3172-1","DOIUrl":"https://doi.org/10.1007/978-1-4612-3172-1","url":null,"abstract":"","PeriodicalId":176863,"journal":{"name":"Springer Series in Computational Mathematics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125188126","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":"History of continued fractions and Pade approximants","authors":"C. Brezinski","doi":"10.1007/978-3-642-58169-4","DOIUrl":"https://doi.org/10.1007/978-3-642-58169-4","url":null,"abstract":"","PeriodicalId":176863,"journal":{"name":"Springer Series in Computational Mathematics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114165250","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":"Numerical continuation methods - an introduction","authors":"E. Allgower, K. Georg","doi":"10.2307/2153001","DOIUrl":"https://doi.org/10.2307/2153001","url":null,"abstract":"1 Introduction.- 2 The Basic Principles of Continuation Methods.- 2.1 Implicitly Defined Curves.- 2.2 The Basic Concepts of PC Methods.- 2.3 The Basic Concepts of PL Methods.- 3 Newton's Method as Corrector.- 3.1 Motivation.- 3.2 The Moore-Penrose Inverse in a Special Case.- 3.3 A Newton's Step for Underdetermined Nonlinear Systems.- 3.4 Convergence Properties of Newton's Method.- 4 Solving the Linear Systems.- 4.1 Using a QR Decomposition.- 4.2 Givens Rotations for Obtaining a QR Decomposition.- 4.3 Error Analysis.- 4.4 Scaling of the Dependent Variables.- 4.5 Using LU Decompositions.- 5 Convergence of Euler-Newton-Like Methods.- 5.1 An Approximate Euler-Newton Method.- 5.2 A Convergence Theorem for PC Methods.- 6 Steplength Adaptations for the Predictor.- 6.1 Steplength Adaptation by Asymptotic Expansion.- 6.2 The Steplength Adaptation of Den Heijer & Rheinboldt.- 6.3 Steplength Strategies Involving Variable Order Predictors.- 7 Predictor-Corrector Methods Using Updating.- 7.1 Broyden's \"Good\" Update Formula.- 7.2 Broyden Updates Along a Curve.- 8 Detection of Bifurcation Points Along a Curve.- 8.1 Simple Bifurcation Points.- 8.2 Switching Branches Via Perturbation.- 8.3 Branching Off Via the Bifurcation Equation.- 9 Calculating Special Points of the Solution Curve.- 9.1 Introduction.- 9.2 Calculating Zero Points f(c(s)) = 0.- 9.3 Calculating Extremal Points minsf((c(s)).- 10 Large Scale Problems.- 10.1 Introduction.- 10.2 General Large Scale Solvers.- 10.3 Nonlinear Conjugate Gradient Methods as Correctors.- 11 Numerically Implementable Existence Proofs.- 11.1 Preliminary Remarks.- 11.2 An Example of an Implementable Existence Theorem.- 11.3 Several Implementations for Obtaining Brouwer Fixed Points.- 11.4 Global Newton and Global Homotopy Methods.- 11.5 Multiple Solutions.- 11.6 Polynomial Systems.- 11.7 Nonlinear Complementarity.- 11.8 Critical Points and Continuation Methods.- 12 PL Continuation Methods.- 12.1 Introduction.- 12.2 PL Approximations.- 12.3 A PL Algorithm for Tracing H(u) = 0.- 12.4 Numerical Implementation of a PL Continuation Algorithm.- 12.5 Integer Labeling.- 12.6 Truncation Errors.- 13 PL Homotopy Algorithms.- 13.1 Set-Valued Maps.- 13.2 Merrill's Restart Algorithm.- 13.3 Some Triangulations and their Implementations.- 13.4 The Homotopy Algorithm of Eaves & Saigal.- 13.5 Mixing PL and Newton Steps.- 13.6 Automatic Pivots for the Eaves-Saigal Algorithm.- 14 General PL Algorithms on PL Manifolds.- 14.1 PL Manifolds.- 14.2 Orientation and Index.- 14.3 Lemke's Algorithm for the Linear Complementarity Problem.- 14.4 Variable Dimension Algorithms.- 14.5 Exploiting Special Structure.- 15 Approximating Implicitly Defined Manifolds.- 15.1 Introduction.- 15.2 Newton's Method and Orthogonal Decompositions Revisited.- 15.3 The Moving Frame Algorithm.- 15.4 Approximating Manifolds by PL Methods.- 15.5 Approximation Estimates.- 16 Update Methods and their Numerical Stability.- 16.1 Introduction.- 16.2 Updates Using the Sherman-Morrison","PeriodicalId":176863,"journal":{"name":"Springer Series in Computational Mathematics","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124816371","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":"Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms","authors":"V. Girault, P. Raviart","doi":"10.1007/978-3-642-61623-5","DOIUrl":"https://doi.org/10.1007/978-3-642-61623-5","url":null,"abstract":"","PeriodicalId":176863,"journal":{"name":"Springer Series in Computational Mathematics","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121394442","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":"Newton-Type Approaches in Finite Dimension","authors":"M. Nakao, M. Plum, Yoshitaka Watanabe","doi":"10.1007/978-981-13-7669-6_2","DOIUrl":"https://doi.org/10.1007/978-981-13-7669-6_2","url":null,"abstract":"","PeriodicalId":176863,"journal":{"name":"Springer Series in Computational Mathematics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116741974","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":"Multi-grid methods and applications","authors":"W. Hackbusch","doi":"10.1007/978-3-662-02427-0","DOIUrl":"https://doi.org/10.1007/978-3-662-02427-0","url":null,"abstract":"","PeriodicalId":176863,"journal":{"name":"Springer Series in Computational Mathematics","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130797411","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":"Basic Principle of the Verification","authors":"M. Nakao, M. Plum, Yoshitaka Watanabe","doi":"10.1007/978-981-13-7669-6_1","DOIUrl":"https://doi.org/10.1007/978-981-13-7669-6_1","url":null,"abstract":"","PeriodicalId":176863,"journal":{"name":"Springer Series in Computational Mathematics","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129546625","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":"Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations","authors":"M. Nakao, M. Plum, Yoshitaka Watanabe","doi":"10.1007/978-981-13-7669-6","DOIUrl":"https://doi.org/10.1007/978-981-13-7669-6","url":null,"abstract":"","PeriodicalId":176863,"journal":{"name":"Springer Series in Computational Mathematics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127643502","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}