Download or read book A Hybrid Pade Galerkin Technique for Differential Equations written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1993 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters. These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated. Perturbation expansions, Pade approximates, Galerkin methods, Hybrid methods, Approximate solutions, Differential equations.
Download or read book A Hybrid Pade Galerkin Technique for Differential Equations written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-28 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated. Geer, James F. and Andersen, Carl M. Unspecified Center NAS1-19480; RTOP 505-90-52-01...
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1966 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Hybrid Perturbation Galerkin Method for Differential Equations Containing a Parameter written by James F. Geer and published by . This book was released on 1989 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monthly Catalogue United States Public Documents written by and published by . This book was released on 1994 with total page 1828 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Elements II written by Alexandre Ern and published by Springer Nature. This book was released on 2021-04-22 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.
Download or read book Monthly Catalog of United States Government Publications written by and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Neural Network Methods for Differential Equations written by Neha Yadav and published by Springer. This book was released on 2015-02-26 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed interest of the 1980s. A general introduction to neural networks and learning technologies is presented in Section III. This section also includes the description of the multilayer perceptron and its learning methods. In Section IV, the different neural network methods for solving differential equations are introduced, including discussion of the most recent developments in the field. Advanced students and researchers in mathematics, computer science and various disciplines in science and engineering will find this book a valuable reference source.
Download or read book A Hybrid perturbation Galerkin Technique which Combines Multiple Expansions written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1989 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Posteriori Error Estimation in Finite Element Analysis written by Mark Ainsworth and published by John Wiley & Sons. This book was released on 2011-09-28 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, one-stop reference-complete with applications This volume presents the most up-to-date information available on aposteriori error estimation for finite element approximation inmechanics and mathematics. It emphasizes methods for ellipticboundary value problems and includes applications to incompressibleflow and nonlinear problems. Recent years have seen an explosion in the study of a posteriorierror estimators due to their remarkable influence on improvingboth accuracy and reliability in scientific computing. In an effortto provide an accessible source, the authors have sought to presentkey ideas and common principles on a sound mathematicalfooting. Topics covered in this timely reference include: * Implicit and explicit a posteriori error estimators * Recovery-based error estimators * Estimators, indicators, and hierarchic bases * The equilibrated residual method * Methodology for the comparison of estimators * Estimation of errors in quantities of interest A Posteriori Error Estimation in Finite Element Analysis is a lucidand convenient resource for researchers in almost any field offinite element methods, and for applied mathematicians andengineers who have an interest in error estimation and/or finiteelements.
Download or read book The Hybrid High Order Method for Polytopal Meshes written by Daniele Antonio Di Pietro and published by Springer Nature. This book was released on 2020-04-03 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion – possibly heterogeneous and anisotropic – and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.
Download or read book Cumulative Reports and Publications Through December 31 1994 written by and published by . This book was released on 1995 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Announcements Index written by and published by . This book was released on 1993-12 with total page 1576 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ground Water Reactive Transport Model Cover Page 03 REVISED eBooks End User License Agreement Website 04 Contents 05 Foreword czheng 06 Preface 07 Contributors 08 Chapter 1 Yeh et al HYDROGEOCHEMA 09 Chapter 2 Wheeler et al IPARS FINAL 10 Chapter 3 Xu et al revised TOUGHREACT 11 Chapter 4 Clement et al RT3D 12 Chapter 5 White et al STOMP ECKEChem 13 Chapter 6 Hammond et al PFLOTRAN 14 Chapter 7 Samper et al CORE2D V4 15 Chapter 8 Mayer et al MIN3P 16 Chapter 9 Hao et al NUFT 17 Index written by Fan Zhang and published by Bentham Science Publishers. This book was released on 2012 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ground water reactive transport models are useful to assess and quantify contaminant precipitation, absorption and migration in subsurface media. Many ground water reactive transport models available today are characterized by varying complexities, strengths, and weaknesses. Selecting accurate, efficient models can be a challenging task. This ebook addresses the needs, issues and challenges relevant to selecting a ground water reactive transport model to evaluate natural attenuation and alternative remediation schemes. It should serve as a handy guide for water resource managers seeking to ach.
Download or read book Fractional Order Analysis written by Hemen Dutta and published by John Wiley & Sons. This book was released on 2020-08-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.
Download or read book Perturbation Methods in Fluid Mechanics written by Milton Van Dyke and published by Parabolic Press, Incorporated. This book was released on 1975 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
