Integral And Integrodifferential Equations

Author : Harendra Singh,Hemen Dutta,Marcelo M. Cavalcanti
Publisher : Springer Nature
Page : 255 pages
File Size : 52,5 Mb
Release : 2021-04-16
Category : Technology & Engineering
ISBN : 9783030655099

Get Book

Topics in Integral and Integro-Differential Equations by Harendra Singh,Hemen Dutta,Marcelo M. Cavalcanti Pdf

This book includes different topics associated with integral and integro-differential equations and their relevance and significance in various scientific areas of study and research. Integral and integro-differential equations are capable of modelling many situations from science and engineering. Readers should find several useful and advanced methods for solving various types of integral and integro-differential equations in this book. The book is useful for graduate students, Ph.D. students, researchers and educators interested in mathematical modelling, applied mathematics, applied sciences, engineering, etc. Key Features • New and advanced methods for solving integral and integro-differential equations • Contains comparison of various methods for accuracy • Demonstrates the applicability of integral and integro-differential equations in other scientific areas • Examines qualitative as well as quantitative properties of solutions of various types of integral and integro-differential equations

Author : Ravi P. Agarwal,Donal O'Regan
Publisher : CRC Press
Page : 344 pages
File Size : 40,5 Mb
Release : 2000-03-09
Category : Mathematics
ISBN : 905699221X

Get Book

Integral and Integrodifferential Equations by Ravi P. Agarwal,Donal O'Regan Pdf

This collection of 24 papers, which encompasses the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm, delay, impulse integral and integro-differential equations in various spaces on bounded as well as unbounded intervals, will conduce and spur further research in this direction.

Author : V. Lakshmikantham
Publisher : CRC Press
Page : 376 pages
File Size : 50,7 Mb
Release : 1995-03-15
Category : Mathematics
ISBN : 2884490000

Get Book

Theory of Integro-Differential Equations by V. Lakshmikantham Pdf

This unique monograph investigates the theory and applications of Volterra integro-differential equations. Whilst covering the basic theory behind these equations it also studies their qualitative properties and discusses a large number of applications. This comprehensive work presents a unified framework to investigate the fundamental existence of theory, treats stability theory in terms of Lyapunov functions and functionals, develops the theory of integro-differential equations with impulse effects, and deals with linear evolution equations in abstract spaces. Various applications of integro-differential equations, such as population dynamics, nuclear reactors, viscoelasticity, wave propagation and engineering systems, are discussed, making this book indispensable for mathematicians and engineers alike.

Author : Vito Volterra
Publisher : Unknown
Page : 316 pages
File Size : 46,6 Mb
Release : 1959
Category : Differential equations
ISBN : UOM:39015000507171

Get Book

Theory of Functionals and of Integral and Integro-differential Equations by Vito Volterra Pdf

Author : Vito Volterra
Publisher : Unknown
Page : 223 pages
File Size : 52,8 Mb
Release : 1944
Category : Electronic
ISBN : OCLC:912240674

Get Book

Theory of Functionals and of Integral and Integro-differential Equations by Vito Volterra Pdf

Author : Donal O'Regan,Maria Meehan
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401149921

Get Book

Existence Theory for Nonlinear Integral and Integrodifferential Equations by Donal O'Regan,Maria Meehan Pdf

The theory of integral and integrodifferential equations has ad vanced rapidly over the last twenty years. Of course the question of existence is an age-old problem of major importance. This mono graph is a collection of some of the most advanced results to date in this field. The book is organized as follows. It is divided into twelve chap ters. Each chapter surveys a major area of research. Specifically, some of the areas considered are Fredholm and Volterra integral and integrodifferential equations, resonant and nonresonant problems, in tegral inclusions, stochastic equations and periodic problems. We note that the selected topics reflect the particular interests of the authors. Donal 0 'Regan Maria Meehan CHAPTER 1 INTRODUCTION AND PRELIMINARIES 1.1. Introduction The aim of this book is firstly to provide a comprehensive existence the ory for integral and integrodifferential equations, and secondly to present some specialised topics in integral equations which we hope will inspire fur ther research in the area. To this end, the first part of the book deals with existence principles and results for nonlinear, Fredholm and Volterra inte gral and integrodifferential equations on compact and half-open intervals, while selected topics (which reflect the particular interests of the authors) such as nonresonance and resonance problems, equations in Banach spaces, inclusions, and stochastic equations are presented in the latter part.

Author : Jurgen Appell,Anatolij Kalitvin,Petr Zabrejko
Publisher : CRC Press
Page : 582 pages
File Size : 47,6 Mb
Release : 2000-02-29
Category : Mathematics
ISBN : 0824703960

Get Book

Partial Integral Operators and Integro-Differential Equations by Jurgen Appell,Anatolij Kalitvin,Petr Zabrejko Pdf

A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linear and nonlinear equations is discussed. Topics range from abstract functional-analytic approaches to specific uses in continuum mechanics and engineering.

Author : Matiur Rahman
Publisher : WIT Press
Page : 385 pages
File Size : 47,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9781845641016

Get Book

Integral Equations and Their Applications by Matiur Rahman Pdf

The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's function as a symmetric kernel of the integral equations.

Author : Svetlin G. Georgiev
Publisher : Springer
Page : 402 pages
File Size : 40,7 Mb
Release : 2016-10-30
Category : Mathematics
ISBN : 9789462392281

Get Book

Integral Equations on Time Scales by Svetlin G. Georgiev Pdf

This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedagogically organized. This book is specially designed for those who wish to understand integral equations on time scales without having extensive mathematical background.

Author : L. M. Delves,J. L. Mohamed
Publisher : CUP Archive
Page : 392 pages
File Size : 50,7 Mb
Release : 1985
Category : Mathematics
ISBN : 0521357969

Get Book

Computational Methods for Integral Equations by L. M. Delves,J. L. Mohamed Pdf

This textbook provides a readable account of techniques for numerical solutions.

Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
Page : 639 pages
File Size : 42,8 Mb
Release : 2011-11-24
Category : Mathematics
ISBN : 9783642214493

Get Book

Linear and Nonlinear Integral Equations by Abdul-Majid Wazwaz Pdf

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 : Theodore Allen Burton
Publisher : Elsevier
Page : 369 pages
File Size : 40,8 Mb
Release : 2005-05-21
Category : Mathematics
ISBN : 9780444517869

Get Book

Volterra Integral and Differential Equations by Theodore Allen Burton Pdf

Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations. This book seeks to present Volterra integral and functional differential equations in that same framwork, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general problems. Thus, the presentation starts slowly with very familiar concepts and shows how these are generalized in a natural way to problems involving a memory. Liapunov's direct method is gently introduced and applied to many particular examples in ordinary differential equations, Volterra integro-differential equations, and functional differential equations. By Chapter 7 the momentum has built until we are looking at problems on the frontier. Chapter 7 is entirely new, dealing with fundamental problems of the resolvent, Floquet theory, and total stability. Chapter 8 presents a solid foundation for the theory of functional differential equations. Many recent results on stability and periodic solutions of functional differential equations are given and unsolved problems are stated. Smooth transition from ordinary differential equations to integral and functional differential equations Unification of the theories, methods, and applications of ordinary and functional differential equations Large collection of examples of Liapunov functions Description of the history of stability theory leading up to unsolved problems Applications of the resolvent to stability and periodic problems

Author : Chen Chuanmiao,Shih Tsimin
Publisher : World Scientific
Page : 292 pages
File Size : 46,6 Mb
Release : 1998-02-28
Category : Mathematics
ISBN : 9789814496957

Get Book

Finite Element Methods for Integrodifferential Equations by Chen Chuanmiao,Shih Tsimin Pdf

Recently, there has appeared a new type of evaluating partial differential equations with Volterra integral operators in various practical areas. Such equations possess new physical and mathematical properties. This monograph systematically discusses application of the finite element methods to numerical solution of integrodifferential equations. It will be useful for numerical analysts, mathematicians, physicists and engineers. Advanced undergraduates and graduate students should also find it beneficial. Contents:Some Practical Problems and Their PropertiesParabolic Integrodifferential EquationsA Survey on Elliptic Finite ElementsSemidiscrete and Fully Discrete SchemesSaving of StorageCases with Nonsmooth Initial ValuesCases with Weakly Singular KernelsLong-Time EstimatesMaximum Norm EstimatesSuperconvergenceNonlinear ProblemsHyperbolic ProblemsProblems with Positive Memory Readership: Researchers in numerical and computational methods. keywords:Introdifferential Equations;Finite Element Method;Semidiscretization;Full Discretization;Maximum Norm Estimate;Superconvergence;Solvability;Integrodifferential Equations;Practical Background;Finite Element Methods;Error Analysis;Ritz-Volterra Projection;Saving of Storage;Nonsmooth Data;Singular Kernel;Parabolic and Hyperbolic;Linear and Nonlinear

Author : Stephen M. Zemyan
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 50,9 Mb
Release : 2012-07-10
Category : Mathematics
ISBN : 9780817683498

Get Book

The Classical Theory of Integral Equations by Stephen M. Zemyan Pdf

The Classical Theory of Integral Equations is a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations. The book provides the background and insight necessary to facilitate a complete understanding of the fundamental results in the field. With a firm foundation for the theory in their grasp, students will be well prepared and motivated for further study. Included in the presentation are: A section entitled Tools of the Trade at the beginning of each chapter, providing necessary background information for comprehension of the results presented in that chapter; Thorough discussions of the analytical methods used to solve many types of integral equations; An introduction to the numerical methods that are commonly used to produce approximate solutions to integral equations; Over 80 illustrative examples that are explained in meticulous detail; Nearly 300 exercises specifically constructed to enhance the understanding of both routine and challenging concepts; Guides to Computation to assist the student with particularly complicated algorithmic procedures. This unique textbook offers a comprehensive and balanced treatment of material needed for a general understanding of the theory of integral equations by using only the mathematical background that a typical undergraduate senior should have. The self-contained book will serve as a valuable resource for advanced undergraduate and beginning graduate-level students as well as for independent study. Scientists and engineers who are working in the field will also find this text to be user friendly and informative.

Author : Abdul-Majid Wazwaz
Publisher : World Scientific
Page : 228 pages
File Size : 49,5 Mb
Release : 1997
Category : Mathematics
ISBN : 9810231016

Get Book

A First Course in Integral Equations by Abdul-Majid Wazwaz Pdf

This book presents the subject of integral equations in an accessible manner for a variety of applications. Emphasis is placed on understanding the subject while avoiding the abstract and compact theorems. A distinctive feature of the book is that it introduces the recent powerful and reliable developments in this field, which are not covered in traditional texts. The newly developed decomposition method, the series solution method and the direct computation method are thoroughly implemented, which allows the topic to be far more accessible. The book also includes some of the traditional techniques for comparison.Using the newly developed methods, the author successfully handles Fredholm and Volterra integral equations, singular integral equations, integro-differential equations and nonlinear integral equations, with promising results for linear and nonlinear models. Many examples are given to introduce the material in a clear and thorough fashion. In addition, many exercises are provided to build confidence, ease and skill in using the new methods.This book may be used as a text for advanced undergraduates and graduate students in mathematics and scientific areas, and as a work of reference for research study of differential equations and numerical analysis.