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The Numerical Solution of Volterra Equations
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.
Volterra Integral Equations
See publisher description :
Collocation Methods for Volterra Integral and Related Functional Differential Equations
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.
Nonlinear Dynamics and Evolution Equations
The papers in this volume reflect a broad spectrum of current research activities on the theory and applications of nonlinear dynamics and evolution equations. They are based on lectures given during the International Conference on Nonlinear Dynamics and Evolution Equations at Memorial University of Newfoundland, St. John's, NL, Canada, July 6-10, 2004. This volume contains thirteen invited and refereed papers. Nine of these are survey papers, introducing the reader to, anddescribing the current state of the art in major areas of dynamical systems, ordinary, functional and partial differential equations, and applications of such equations in the mathematical modelling of various biological and physical phenomena. These papers are complemented by four research papers thatexamine particular problems in the theory and applications of dynamical systems. Information for our distributors: Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
The Long Road to Stockholm
In this autobiography, Sir Peter Mansfield describes his life from war time childhood that initially sparked his interest in physics to his work in magnetic resonance imaging (MRI) that eventually led to the award of the Nobel Prize in 2003. Peter Mansfield grew up in London, but was evacuated to Devon during the blitz and following the V1 and V2 attacks on London. At the end of hostilities, he worked briefly in the printing industry before deciding to pursue his real interests in science by joining the Rocket Propulsion Department at Westcott near Aylesbury. Following a period of National Service and his studies at Queen Mary College, University of London, he married and moved to the USA fo...
The Apocalypse Syndrome
When writer Hammond Sinclair arrives in Geneva to follow the World Climate Conference at first hand, he is not only interested in the global warming controversy. He suspects that a former student of his, now a right-wing extremist, is plotting a spectacular terrorist attack to disrupt the summit. In a city overrun by rival mobs of violent demonstrators from all over Europe, he meets a young anarchist girl, and in order to impress her takes part in a public debate. It plunges him into the maelstrom of an ideological conflict with high stakes, where opposing sides have their own visions of apocalypse, and are prepared to do anything to save humanity from the catastrophe they foresee. Chief Com...
Difference and Differential Equations
This volume contains papers from the 7th International Conference on Difference Equations held at Hunan University (Changsa, China), a satellite conference of ICM2002 Beijing. The volume captures the spirit of the meeting and includes peer-reviewed survey papers, research papers, and open problems and conjectures. Articles cover stability, oscillation, chaos, symmetries, boundary value problems and bifurcations for discrete dynamical systems, difference-differential equations, and discretization of continuous systems. The book presents state-of-the-art research in these important areas. It is suitable for graduate students and researchers in difference equations and related topics.
