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Author : Hermann Brunner
Publisher : Cambridge University Press
Page : 620 pages
File Size : 49,8 Mb
Release : 2004-11-15
Category : Mathematics
ISBN : 0521806151
Publisher Description
Author : Hermann Brunner
Publisher : Cambridge University Press
Page : 405 pages
File Size : 49,7 Mb
Release : 2017-01-20
Category : Mathematics
ISBN : 9781107098725
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Author : Hermann Brunner,Pieter Jacobus Houwen
Publisher : North Holland
Page : 608 pages
File Size : 45,9 Mb
Release : 1986
Category : Mathematics
ISBN : UCAL:B4406086
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.
Author : Burton
Publisher : Academic Press
Page : 312 pages
File Size : 45,6 Mb
Release : 1983-11-04
Category : Computers
ISBN : 9780080956732
Volterra Integral and Differential Equations
Author : G. Gripenberg,S. O. Londen,O. Staffans
Publisher : Cambridge University Press
Page : 727 pages
File Size : 54,5 Mb
Release : 1990
Category : Mathematics
ISBN : 9780521372893
This book looks at the theories of Volterra integral and functional equations.
Author : Henry Ekah-Kunde
Publisher : GRIN Verlag
Page : 26 pages
File Size : 53,8 Mb
Release : 2017-07-17
Category : Mathematics
ISBN : 9783668484269
Seminar paper from the year 2015 in the subject Mathematics - Applied Mathematics, grade: A, , language: English, abstract: In scientific and engineering problems Volterra integral equations are always encountered. Applications of Volterra integral equations arise in areas such as population dynamics, spread of epidemics in the society, etc. The problem statement is to obtain a good numerical solution to such an integral equation. A brief theory of Volterra Integral equation, particularly, of weakly singular types, and a numerical method, the collocation method, for solving such equations, in particular Volterra integral equation of second kind, is handled in this paper. The principle of this method is to approximate the exact solution of the equation in a suitable finite dimensional space. The approximating space considered here is the polynomial spline space. In the treatment of the collocation method emphasis is laid, during discretization, on the mesh type. The approximating space applied here is the polynomial spline space. The discrete convergence properties of spline collocation solutions for certain Volterra integral equations with weakly singular kernels shall is analyzed. The order of convergence of spline collocation on equidistant mesh points is also compared with approximation on graded meshes. In particular, the attainable convergence orders at the collocation points are examined for certain choices of the collocation parameters.
Author : Kenneth B. Hannsgen
Publisher : CRC Press
Page : 356 pages
File Size : 51,6 Mb
Release : 1982-10-25
Category : Mathematics
ISBN : 082471721X
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 : Peter Linz
Publisher : SIAM
Page : 240 pages
File Size : 43,5 Mb
Release : 1985-01-01
Category : Mathematics
ISBN : 1611970857
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.
Author : Kenneth B. Hannsgen
Publisher : CRC Press
Page : 352 pages
File Size : 50,8 Mb
Release : 2023-05-31
Category : Mathematics
ISBN : 9781000942316
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 : Harendra Singh,Hemen Dutta,Marcelo M. Cavalcanti
Publisher : Springer Nature
Page : 255 pages
File Size : 52,7 Mb
Release : 2021-04-16
Category : Technology & Engineering
ISBN : 9783030655099
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 : C. Corduneanu
Publisher : CRC Press
Page : 185 pages
File Size : 50,6 Mb
Release : 2002-09-05
Category : Mathematics
ISBN : 9780203166376
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with cau
Author : Henry Ekah-Kunde
Publisher : GRIN Verlag
Page : 23 pages
File Size : 41,5 Mb
Release : 2017-07-28
Category : Mathematics
ISBN : 9783668494152
Seminar paper from the year 2015 in the subject Mathematics - Applied Mathematics, grade: A, , language: English, abstract: In this research, a novel method to approximate the solution of optimal control problems governed by Volterra integral equations of weakly singular types is proposed. The method introduced here is the conjugate gradient method with a discretization of the problem based on the collocation approach on graded mesh points for non linear Volterra integral equations with singular kernels. Necessary and sufficient optimality conditions for optimal control problems are also discussed. Some examples are presented to demonstrate the efficiency of the method.
Author : Mare Tarang
Publisher : Unknown
Page : 98 pages
File Size : 52,5 Mb
Release : 2004
Category : Differential equations
ISBN : UOM:39015079135920
Author : C. Corduneanu,I Sandberg
Publisher : CRC Press
Page : 522 pages
File Size : 54,5 Mb
Release : 2000-01-10
Category : Mathematics
ISBN : 905699171X
This volume comprises selected papers presented at the Volterra Centennial Symposium and is dedicated to Volterra and the contribution of his work to the study of systems - an important concept in modern engineering. Vito Volterra began his study of integral equations at the end of the nineteenth century and this was a significant development in the theory of integral equations and nonlinear functional analysis. Volterra series are of interest and use in pure and applied mathematics and engineering.
Author : Arthur G. Werschulz
Publisher : Unknown
Page : 352 pages
File Size : 47,7 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015024770268
Complexity theory has become an increasingly important theme in mathematical research. This book deals with an approximate solution of differential or integral equations by algorithms using incomplete information. This situation often arises for equations of the form Lu = f where f is some function defined on a domain and L is a differential operator. We do not have complete information about f. For instance, we might only know its value at a finite number of points in the domain, or the values of its inner products with a finite set of known functions. Consequently the best that can be hoped for is to solve the equation to within a given accuracy at minimal cost or complexity. In this book, the theory of the complexity of the solution to differential and integral equations is developed. The relationship between the worst case setting and other (sometimes more tractable) related settings, such as the average case, probabilistic, asymptotic, and randomized settings, is also discussed. The author determines the inherent complexity of the problem and finds optimal algorithms (in the sense of having minimal cost). Furthermore, he studies to what extent standard algorithms (such as finite element methods for elliptic problems) are optimal. This approach is discussed in depth in the context of two-point boundary value problems, linear elliptic partial differential equations, integral equations, ordinary differential equations, and ill-posed problems. As a result, this volume should appeal to mathematicians and numerical analysts working on the approximate solution of differential and integral equations, as well as to complexity theorists addressing related questions in this area.
