Analytical and Numerical Methods for Volterra Equations

Analytical and Numerical Methods for Volterra Equations
Author: Peter Linz
Publisher: SIAM
Total Pages: 240
Release: 1985-01-01
Genre: Mathematics
ISBN: 9781611970852

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.

Volterra Integral Equations

Volterra Integral Equations
Author: Hermann Brunner
Publisher: Cambridge University Press
Total Pages: 405
Release: 2017-01-20
Genre: Mathematics
ISBN: 1107098726

See publisher description :

Volterra Integral and Functional Equations

Volterra Integral and Functional Equations
Author: G. Gripenberg
Publisher: Cambridge University Press
Total Pages: 727
Release: 1990
Genre: Mathematics
ISBN: 0521372895

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

Collocation Methods for Volterra Integral and Related Functional Differential Equations

Collocation Methods for Volterra Integral and Related Functional Differential Equations
Author: Hermann Brunner
Publisher: Cambridge University Press
Total Pages: 620
Release: 2004-11-15
Genre: Mathematics
ISBN: 9780521806152

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.

Volterra Equations and Inverse Problems

Volterra Equations and Inverse Problems
Author: A. L. Bughgeim
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 216
Release: 2014-07-24
Genre: Mathematics
ISBN: 3110943247

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Linear and Nonlinear Integral Equations

Linear and Nonlinear Integral Equations
Author: Abdul-Majid Wazwaz
Publisher: Springer Science & Business Media
Total Pages: 639
Release: 2011-11-24
Genre: Mathematics
ISBN: 3642214495

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.

The Numerical Solution of Volterra Equations

The Numerical Solution of Volterra Equations
Author: Hermann Brunner
Publisher: North Holland
Total Pages: 608
Release: 1986
Genre: Mathematics
ISBN:

This monograph presents the theory and modern numerical analysis of Volterra integral and integro-differential equations, including equations with weakly singular kernels. While the research worker will find an up-to-date account of recent developments of numerical methods for such equations, including an extensive bibliography, the authors have tried to make the book accessible to the non-specialist possessing only a limited knowledge of numerical analysis. After an introduction to the theory of Volterra equations and to numerical integration, the book covers linear methods and Runge-Kutta methods, collocation methods based on polynomial spline functions, stability of numerical methods, and it surveys computer programs for Volterra integral and integro-differential equations.

Abstract Volterra Integro-Differential Equations

Abstract Volterra Integro-Differential Equations
Author: Marko Kostic
Publisher:
Total Pages: 0
Release: 2019-09-19
Genre:
ISBN: 9780367377670

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.

Handbook of Integral Equations

Handbook of Integral Equations
Author: Andrei D. Polyanin
Publisher: CRC Press
Total Pages: 1143
Release: 2008-02-12
Genre: Mathematics
ISBN: 0203881052

Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa

Modelling with Differential and Difference Equations

Modelling with Differential and Difference Equations
Author: Glenn Fulford
Publisher: Cambridge University Press
Total Pages: 420
Release: 1997-06-12
Genre: Mathematics
ISBN: 9780521446181

Any student wishing to solve problems via mathematical modelling will find that this book provides an excellent introduction to the subject.