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Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 9780521806152
Category : Mathematics
Languages : en
Pages : 620
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Book Description
Publisher Description
Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 9780521806152
Category : Mathematics
Languages : en
Pages : 620
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Book Description
Publisher Description
Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 1316982653
Category : Mathematics
Languages : en
Pages : 405
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Book Description
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.
Author: Theodore Allen Burton
Publisher: Elsevier
ISBN: 0444517863
Category : Mathematics
Languages : en
Pages : 369
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Book Description
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: Hermann Brunner
Publisher: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 608
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Book Description
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
ISBN: 0080956734
Category : Computers
Languages : en
Pages : 312
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Book Description
Volterra Integral and 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: Henry Ekah-Kunde
Publisher: GRIN Verlag
ISBN: 3668484260
Category : Mathematics
Languages : en
Pages : 26
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Book Description
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
ISBN: 9780824717216
Category : Mathematics
Languages : en
Pages : 356
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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: Mare Tarang
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 98
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Book Description
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.
