Exponentially Convergent Algorithms For Abstract Differential Equations
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Exponentially Convergent Algorithms for Abstract Differential Equations
Author: Ivan Gavrilyuk
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-07-17
This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which then can be applied to mathematical models of the real world. The problem class includes initial value problems (IVP) for first order differential equations with constant and variable unbounded operator coefficients in a Banach space (the heat equation is a simple example), boundary value problems for the second order elliptic differential equation with an operator coefficient (e.g. the Laplace equation), IVPs for the second order strongly damped differential equation as well as exponentially convergent methods to IVPs for the first order nonlinear differential equation with unbounded operator coefficients. For researchers and students of numerical functional analysis, engineering and other sciences this book provides highly efficient algorithms for the numerical solution of differential equations and applied problems.
Analytical and Approximate Methods for Complex Dynamical Systems
This book presents Analytical and Approximate Methods for Complex Dynamical Systems and introduces ideas of discontinuous mapping treated as complex dynamical systems. Mathematicians of world-recognized Ukrainian scientific schools established by M.Krylov, M.Bogolyubov, Yu.Mitropolskiy, and A.Sharkovsky used to cooperate for writing the collective book whose purpose consists of illustrating a synergy of combining diverse (by idea and technique) constructive analytical and approximate approaches and methods in complex dynamical systems which are herein associated with mathematical models of networks, conflict/economic theories, sloshing, soft matter, and even levitating drops. Readers are facilitated to learn contemporary insights, fundamentals (Parts I and III), applications (Part II), and components of theories of bifurcation, synchronization/self-organization, collective dynamics, chaos, solitons, fractional differential equations, symmetry, reduced order modelling, and many others, that makes the book useful for both graduate and postgraduate students, lecturers, researchers, and even engineers dealing with multidimensional dynamic systems.
Modern Analysis and Applications
Author: Vadim Adamyan
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-08-29
This is the second of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.