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Numerical Hamiltonian Problems
Advanced text explores mathematical problems that occur frequently in physics and other sciences. Topics include symplectic integration, symplectic order conditions, available symplectic methods, numerical experiments, properties of symplectic integrators. 1994 edition.
Current Challenges in Stability Issues for Numerical Differential Equations
This volume addresses some of the research areas in the general field of stability studies for differential equations, with emphasis on issues of concern for numerical studies. Topics considered include: (i) the long time integration of Hamiltonian Ordinary DEs and highly oscillatory systems, (ii) connection between stochastic DEs and geometric integration using the Markov chain Monte Carlo method, (iii) computation of dynamic patterns in evolutionary partial DEs, (iv) decomposition of matrices depending on parameters and localization of singularities, and (v) uniform stability analysis for time dependent linear initial value problems of ODEs. The problems considered in this volume are of interest to people working on numerical as well as qualitative aspects of differential equations, and it will serve both as a reference and as an entry point into further research.
Riemannian Geometric Statistics in Medical Image Analysis
Over the past 15 years, there has been a growing need in the medical image computing community for principled methods to process nonlinear geometric data. Riemannian geometry has emerged as one of the most powerful mathematical and computational frameworks for analyzing such data. Riemannian Geometric Statistics in Medical Image Analysis is a complete reference on statistics on Riemannian manifolds and more general nonlinear spaces with applications in medical image analysis. It provides an introduction to the core methodology followed by a presentation of state-of-the-art methods. Content includes: - The foundations of Riemannian geometric methods for statistics on manifolds with emphasis o...
Numerical Approximation of Ordinary Differential Problems
This book is focused on the numerical discretization of ordinary differential equations (ODEs), under several perspectives. The attention is first conveyed to providing accurate numerical solutions of deterministic problems. Then, the presentation moves to a more modern vision of numerical approximation, oriented to reproducing qualitative properties of the continuous problem along the discretized dynamics over long times. The book finally performs some steps in the direction of stochastic differential equations (SDEs), with the intention of offering useful tools to generalize the techniques introduced for the numerical approximation of ODEs to the stochastic case, as well as of presenting n...
Numerical Analysis of Multiscale Computations
This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and fast multipole method.
Computational Methods for Risk Management in Economics and Finance
At present, computational methods have received considerable attention in economics and finance as an alternative to conventional analytical and numerical paradigms. This Special Issue brings together both theoretical and application-oriented contributions, with a focus on the use of computational techniques in finance and economics. Examined topics span on issues at the center of the literature debate, with an eye not only on technical and theoretical aspects but also very practical cases.
