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Collocation Methods For Weakly Singular Volterra Integral Equations With Vanishing Delays
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Book Synopsis Collocation Methods for Volterra Integral and Related Functional Differential Equations by : Hermann Brunner
Download or read book Collocation Methods for Volterra Integral and Related Functional Differential Equations written by Hermann Brunner and published by Cambridge University Press. This book was released on 2004-11-15 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory terms, delay equations, and differential-algebraic and integral-algebraic equations. Each chapter starts with a self-contained introduction to the relevant theory of the class of equations under consideration. Numerous exercises and examples are supplied, along with extensive historical and bibliographical notes utilising the vast annotated reference list of over 1300 items. In sum, Hermann Brunner has written a treatise that can serve as an introduction for students, a guide for users, and a comprehensive resource for experts.
Book Synopsis Volterra Integral Equations by : Hermann Brunner
Download or read book Volterra Integral Equations written by Hermann Brunner and published by Cambridge University Press. This book was released on 2017-01-20 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a 'stepping stone' to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.
Download or read book Spectral Methods written by Jie Shen and published by Springer Science & Business Media. This book was released on 2011-08-25 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.
Book Synopsis Multidimensional Weakly Singular Integral Equations by : Gennadi Vainikko
Download or read book Multidimensional Weakly Singular Integral Equations written by Gennadi Vainikko and published by Springer. This book was released on 2006-11-15 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final aim of the book is to construct effective discretization methods to solve multidimensional weakly singular integral equations of the second kind on a region of Rn e.g. equations arising in the radiation transfer theory. To this end, the smoothness of the solution is examined proposing sharp estimates of the growth of the derivatives of the solution near the boundary G. The superconvergence effect of collocation methods at the collocation points is established. This is a book for graduate students and researchers in the fields of analysis, integral equations, mathematical physics and numerical methods. No special knowledge beyond standard undergraduate courses is assumed.
Book Synopsis Solving ODEs with MATLAB by : Lawrence F. Shampine
Download or read book Solving ODEs with MATLAB written by Lawrence F. Shampine and published by Cambridge University Press. This book was released on 2003-04-28 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.
Book Synopsis Numerical Methods for Delay Differential Equations by : Alfredo Bellen
Download or read book Numerical Methods for Delay Differential Equations written by Alfredo Bellen and published by Numerical Mathematics and Scie. This book was released on 2013-01-10 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book describes, analyses, and improves various approaches and techniques for the numerical solution of delay differential equations. It includes a list of available codes and also aids the reader in writing his or her own.
Book Synopsis Spectral and High-order Methods with Applications by : Jie Shen
Download or read book Spectral and High-order Methods with Applications written by Jie Shen and published by . This book was released on 2006 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 中国科学院科学出版基金资助出版。
Book Synopsis Linear and Nonlinear Integral Equations by : Abdul-Majid Wazwaz
Download or read book Linear and Nonlinear Integral Equations written by Abdul-Majid Wazwaz and published by Springer Science & Business Media. This book was released on 2011-11-24 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.
Book Synopsis New Trends in Differential and Difference Equations and Applications by : Feliz Manuel Minhós
Download or read book New Trends in Differential and Difference Equations and Applications written by Feliz Manuel Minhós and published by MDPI. This book was released on 2019-10-14 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.
Book Synopsis Introduction to Integral Equations with Applications by : Abdul J. Jerri
Download or read book Introduction to Integral Equations with Applications written by Abdul J. Jerri and published by . This book was released on 1985 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abdul Jerri has revised his highly applied book to make it even more useful for scientists and engineers, as well as mathematicians. Covering the fundamental ideas and techniques at a level accessible to anyone with a solid undergraduate background in calculus and differential equations, Dr. Jerri clearly demonstrates how to use integral equations to solve real-world engineering and physics problems. This edition provides precise guidelines to the basic methods of solutions, details more varied numerical methods, and substantially boosts the total of practical examples and exercises. Plus, it features added emphasis on the basic theorems for the existence and uniqueness of solutions of integral equations and points out the interrelation between differentiation and integration.
Book Synopsis Weighted Inequalities of Hardy Type by : Alois Kufner
Download or read book Weighted Inequalities of Hardy Type written by Alois Kufner and published by World Scientific. This book was released on 2003 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new fields such as higher order and fractional order Hardy type inequalities and integral inequalities on the cone of monotone functions together with some applications and open problems. The book can serve as a reference and a source of inspiration for researchers working in these and related areas, but could also be used for advanced graduate courses.
Author :Dragoslav S. Mitrinovic Publisher :Springer Science & Business Media ISBN 13 :9780792313304 Total Pages :606 pages Book Rating :4.3/5 (133 download)
Book Synopsis Inequalities Involving Functions and Their Integrals and Derivatives by : Dragoslav S. Mitrinovic
Download or read book Inequalities Involving Functions and Their Integrals and Derivatives written by Dragoslav S. Mitrinovic and published by Springer Science & Business Media. This book was released on 1991-07-31 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive, up-to-date survey of inequalities that involve a relationship between a function and its derivatives or integrals. The book is divided into 18 chapters, some of which are devoted to specific inequalities such as those of Kolmogorov-Landau, Wirtinger, Hardy, Carlson, Hilbert, Caplygin, Lyapunov, Gronwell and others. Over 800 references to the literature are cited; proofs are given when these provide insight into the general methods involved; and applications, especially to the theory of differential equations, are mentioned when appropriate. This volume will interest all those whose work involves differential and integral equations. It can also be recommended as a supplementary text.
Book Synopsis Acta Numerica 2004: Volume 13 by : Arieh Iserles
Download or read book Acta Numerica 2004: Volume 13 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2004-06-03 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: An annual volume presenting substantive survey articles in numerical mathematics and scientific computing.
Book Synopsis Spectral Methods by : Claudio Canuto
Download or read book Spectral Methods written by Claudio Canuto and published by Springer Science & Business Media. This book was released on 2007-09-23 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.
Book Synopsis Analytical and Numerical Methods for Volterra Equations by : Peter Linz
Download or read book Analytical and Numerical Methods for Volterra Equations written by Peter Linz and published by SIAM. This book was released on 1985-01-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.
Book Synopsis Galerkin Finite Element Methods for Parabolic Problems by : Vidar Thomee
Download or read book Galerkin Finite Element Methods for Parabolic Problems written by Vidar Thomee and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.
Book Synopsis Computational Fluid and Solid Mechanics 2003 by : K.J Bathe
Download or read book Computational Fluid and Solid Mechanics 2003 written by K.J Bathe and published by Elsevier. This book was released on 2003-06-02 with total page 2485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing together the world's leading researchers and practitioners of computational mechanics, these new volumes meet and build on the eight key challenges for research and development in computational mechanics.Researchers have recently identified eight critical research tasks facing the field of computational mechanics. These tasks have come about because it appears possible to reach a new level of mathematical modelling and numerical solution that will lead to a much deeper understanding of nature and to great improvements in engineering design.The eight tasks are: - The automatic solution of mathematical models - Effective numerical schemes for fluid flows - The development of an effective mesh-free numerical solution method - The development of numerical procedures for multiphysics problems - The development of numerical procedures for multiscale problems - The modelling of uncertainties - The analysis of complete life cycles of systems - Education - teaching sound engineering and scientific judgement Readers of Computational Fluid and Solid Mechanics 2003 will be able to apply the combined experience of many of the world's leading researchers to their own research needs. Those in academic environments will gain a better insight into the needs and constraints of the industries they are involved with; those in industry will gain a competitive advantage by gaining insight into the cutting edge research being carried out by colleagues in academia. Features - Bridges the gap between academic researchers and practitioners in industry - Outlines the eight main challenges facing Research and Design in Computational mechanics and offers new insights into the shifting the research agenda - Provides a vision of how strong, basic and exciting education at university can be harmonized with life-long learning to obtain maximum value from the new powerful tools of analysis
