Difference Equations In Normed Spaces, Volume 206: Stability And Oscillations (north-holland Mathematics Studies)
by Michael Gil /
2007 / English / PDF
7.2 MB Download
Difference equations appear as natural descriptions of observed
evolution phenomena because most measurements of time evolving
variables are discrete. They also appear in the applications of
discretization methods for differential, integral and
integro-differential equations.
Difference equations appear as natural descriptions of observed
evolution phenomena because most measurements of time evolving
variables are discrete. They also appear in the applications of
discretization methods for differential, integral and
integro-differential equations.
The application of the theory of difference equations is rapidly
increasing to various fields, such as numerical analysis, control
theory, finite mathematics, and computer sciences. This book is
devoted to linear and nonlinear difference equations in a normed
space. The main methodology presented in this book is based on a
combined use of recent norm estimates for operator-valued
functions with the following methods and results:
The application of the theory of difference equations is rapidly
increasing to various fields, such as numerical analysis, control
theory, finite mathematics, and computer sciences. This book is
devoted to linear and nonlinear difference equations in a normed
space. The main methodology presented in this book is based on a
combined use of recent norm estimates for operator-valued
functions with the following methods and results:The freezing method
The freezing methodThe Liapunov type equation
The Liapunov type equationThe method of majorants
The method of majorantsThe multiplicative representation of solutions
The multiplicative representation of solutionsDeals systematically with difference equations in normed
spaces
Deals systematically with difference equations in normed
spacesConsiders new classes of equations that could not be studied
in the frameworks of ordinary and partial difference equations
Considers new classes of equations that could not be studied
in the frameworks of ordinary and partial difference equationsDevelops the freezing method and presents recent results on
Volterra discrete equations
Develops the freezing method and presents recent results on
Volterra discrete equationsContains an approach based on the estimates for norms of
operator functions
Contains an approach based on the estimates for norms of
operator functions
