Collocation Methods for Volterra Integral and Related Functional Differential Equations PDF Download

Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 9780521806152
Category : Mathematics
Languages : en
Pages : 620

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Book Description
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.

Author: Kenneth B. Hannsgen
Publisher: CRC Press
ISBN: 1000942317
Category : Mathematics
Languages : en
Pages : 352

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Book Description
This book contains twenty four papers, presented at the conference on Volterra and Functional Differential Equations held in Virginia in 1981, on various topics, including Liapunov stability, Volterra equations, integral equations, and functional differential equations.

Author: G. Gripenberg
Publisher: Cambridge University Press
ISBN: 0521372895
Category : Mathematics
Languages : en
Pages : 727

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Book Description
This book looks at the theories of Volterra integral and functional equations.

Author: Klaus Schmitt
Publisher: Elsevier
ISBN: 1483272338
Category : Mathematics
Languages : en
Pages : 414

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Book Description
Delay and Functional Differential Equations and Their Applications provides information pertinent to the fundamental aspects of functional differential equations and its applications. This book covers a variety of topics, including qualitative and geometric theory, control theory, Volterra equations, numerical methods, the theory of epidemics, problems in physiology, and other areas of applications. Organized into two parts encompassing 25 chapters, this book begins with an overview of problems involving functional differential equations with terminal conditions in function spaces. This text then examines the numerical methods for functional differential equations. Other chapters consider the theory of radiative transfer, which give rise to several interesting functional partial differential equations. This book discusses as well the theory of embedding fields, which studies systems of nonlinear functional differential equations that can be derived from psychological postulates and interpreted as neural networks. The final chapter deals with the usefulness of the flip-flop circuit. This book is a valuable resource for mathematicians.

Author: Vito Volterra
Publisher: Courier Dover Publications
ISBN: 9780486442846
Category : Differential equations
Languages : en
Pages : 0

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Book Description
A classic work by the mathematician who developed the general theory of functions that depend on a continuous set of values of another function, this volume deals primarily with integral equations.

Author: Liu
Publisher: CRC Press
ISBN: 9780824792701
Category : Mathematics
Languages : en
Pages : 390

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Book Description
This work is based on the International Symposium on Comparison Methods and Stability Theory held in Waterloo, Ontario, Canada. It presents advances in comparison methods and stability theory in a wide range of nonlinear problems, covering a variety of topics such as ordinary, functional, impulsive, integro-, partial, and uncertain differential equations.

Author: Abdul-Majid Wazwaz
Publisher: Springer Science & Business Media
ISBN: 3642214495
Category : Mathematics
Languages : en
Pages : 639

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Book Description
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.

Author: Harlan W. Stech
Publisher: CRC Press
ISBN: 9780824713546
Category : Mathematics
Languages : en
Pages : 298

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Book Description

Author: Marko Kostic
Publisher:
ISBN: 9780367377670
Category :
Languages : en
Pages : 0

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Book Description
The theory of linear Volterra Integro-differental equations has been developing rapidly in the last three decades. This book provides an easy-to-read, concise introduction to the theory of ill-posed abstract Volterra Integro-differential equations. It is accessible to readers whose backgrounds include functions of one complex variable, integration theory and the basic theory of locally convex spaces. Each chapter is further divided into sections and subsections, and contains plenty of examples and open problems.

Author: T. A. Burton
Publisher: Courier Corporation
ISBN: 0486150453
Category : Mathematics
Languages : en
Pages : 370

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Book Description
This book's discussion of a broad class of differential equations includes linear differential and integrodifferential equations, fixed-point theory, and the basic stability and periodicity theory for nonlinear ordinary and functional differential equations.