This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulted as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage...
This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the...
This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulted as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage...
This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the...
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and s- bolic computer systems, dynamical systems, and...
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disci...
On 6 June 1944 British, American, Canadian and French troops landed in Normandy by air and sea. This was one of the key moments of the Second World War, a long-anticipated invasion which would, ultimately, lead to the defeat of Nazi Germany. By the day's end a lodgment had been effected and Operation OVERLORD was being hailed as a success.
In reality the assault had produced mixed results and at certain points along the French coastline the position was still far from certain. The key Allied objectives had also not been captured during the first day of the fighting and this failure...
On 6 June 1944 British, American, Canadian and French troops landed in Normandy by air and sea. This was one of the key moments of the Second World Wa...
This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online.
The book is organized into...
This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and comp...