High Order Difference Methods for Time Dependent PDE PDF Download

Author: Bertil Gustafsson
Publisher: Springer Science & Business Media
ISBN: 3540749934
Category : Mathematics
Languages : en
Pages : 343

View

Book Description
This book covers high order finite difference methods for time dependent PDE. It gives an overview of the basic theory and construction principles by using model examples. The book also contains a general presentation of the techniques and results for well-posedness and stability, with inclusion of the three fundamental methods of analysis both for PDE in its original and discretized form: the Fourier transform, the eneregy method and the Laplace transform.

Author: Alouf Jirari
Publisher: American Mathematical Soc.
ISBN: 082180359X
Category : Mathematics
Languages : en
Pages : 154

View

Book Description
This memoir presents machinery for analyzing many discrete physical situations, and should be of interest to physicists, engineers, and mathematicians. We develop a theory for regular and singular Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. We discuss the self-adjointness of these problems as well as their abstract spectral resolution in the appropriate [italic capital]L2 setting, and give necessary and sufficient conditions for a second-order difference operator to be self-adjoint and have orthogonal polynomials as eigenfunctions.

Author: V.L. Kocic
Publisher: Springer Science & Business Media
ISBN: 9401717036
Category : Mathematics
Languages : en
Pages : 237

View

Book Description
Nonlinear difference equations of order greater than one are of paramount impor tance in applications where the (n + 1)st generation (or state) of the system depends on the previous k generations (or states). Such equations also appear naturally as discrete analogues and as numerical solutions of differential and delay differential equations which model various diverse phenomena in biology, ecology, physiology, physics, engineering and economics. Our aim in this monograph is to initiate a systematic study of the global behavior of solutions of nonlinear scalar difference equations of order greater than one. Our primary concern is to study the global asymptotic stability of the equilibrium solution. We are also interested in whether the solutions are bounded away from zero and infinity, in the description of the semi cycles of the solutions, and in the existence of periodic solutions. This monograph contains some recent important developments in this area together with some applications to mathematical biology. Our intention is to expose the reader to the frontiers of the subject and to formulate some important open problems that require our immediate attention.

Author: Mustafa R.S. Kulenovic
Publisher: CRC Press
ISBN: 142003538X
Category : Mathematics
Languages : en
Pages : 235

View

Book Description
This self-contained monograph provides systematic, instructive analysis of second-order rational difference equations. After classifying the various types of these equations and introducing some preliminary results, the authors systematically investigate each equation for semicycles, invariant intervals, boundedness, periodicity, and global stabili

Author: James Williams
Publisher: Edinburgh University Press
ISBN: 0748668950
Category : Philosophy
Languages : en
Pages : 273

View

Book Description
A new edition of this introduction to Deleuze's seminal work, Difference and Repetition, with new material on intensity, science and action and new engagements with Bryant, Sauvagnargues, Smith, Somers-Hall and de Beistegui.

Author: Samuel Goldberg
Publisher: Courier Corporation
ISBN: 0486650847
Category : Mathematics
Languages : en
Pages : 292

View

Book Description
Exceptionally clear exposition of an important mathematical discipline and its applications to sociology, economics, and psychology. Topics include calculus of finite differences, difference equations, matrix methods, and more. 1958 edition.

Author: Saber N. Elaydi
Publisher: Springer Science & Business Media
ISBN: 1475791682
Category : Mathematics
Languages : en
Pages : 398

View

Book Description
This book grew out of lecture notes I used in a course on difference equations that I taught at Trinity University for the past five years. The classes were largely pop ulated by juniors and seniors majoring in Mathematics, Engineering, Chemistry, Computer Science, and Physics. This book is intended to be used as a textbook for a course on difference equations at the level of both advanced undergraduate and beginning graduate. It may also be used as a supplement for engineering courses on discrete systems and control theory. The main prerequisites for most of the material in this book are calculus and linear algebra. However, some topics in later chapters may require some rudiments of advanced calculus. Since many of the chapters in the book are independent, the instructor has great flexibility in choosing topics for the first one-semester course. A diagram showing the interdependence of the chapters in the book appears following the preface. This book presents the current state of affairs in many areas such as stability, Z-transform, asymptoticity, oscillations and control theory. However, this book is by no means encyclopedic and does not contain many important topics, such as Numerical Analysis, Combinatorics, Special functions and orthogonal polyno mials, boundary value problems, partial difference equations, chaos theory, and fractals. The nonselection of these topics is dictated not only by the limitations imposed by the elementary nature of this book, but also by the research interest (or lack thereof) of the author.

Author: S.K. Godunov
Publisher: Elsevier
ISBN: 0080875408
Category : Mathematics
Languages : en
Pages : 509

View

Book Description
Much applied and theoretical research in natural sciences leads to boundary-value problems stated in terms of differential equations. When solving these problems with computers, the differential problems are replaced approximately by difference schemes.This book is an introduction to the theory of difference schemes, and was written as a textbook for university mathematics and physics departments and for technical universities. Some sections of the book will be of interest to computations specialists.While stressing a mathematically rigorous treatment of model problems, the book also demonstrates the relation between theory and computer experiments, using difference schemes created for practical computations.

Author: Kareem Khalifa
Publisher: Cambridge University Press
ISBN: 1107195632
Category : Philosophy
Languages : en
Pages : 265

View

Book Description
The first comprehensive exploration of the nature and value of understanding, addressing burgeoning debates in epistemology and philosophy of science.

Author: Aleksandra Gruszka
Publisher: Springer Science & Business Media
ISBN: 9781441912107
Category : Psychology
Languages : en
Pages : 494

View

Book Description
As cognitive models of behavior continue to evolve, the mechanics of cognitive exceptionality, with its range of individual variations in abilities and performance, remains a challenge to psychology. Reaching beyond the standard view of exceptional cognition equaling superior intelligence, the Handbook of Individual Differences in Cognition examines the latest findings from psychobiology, cognitive psychology, and neuroscience, for a comprehensive state-of-the-art volume. Breaking down cognition in terms of attentional mechanisms, working memory, and higher-order processing, contributors discuss general models of cognition and personality. Chapter authors build on this foundation as they revisit current theory in such areas as processing effort and general arousal and examine emerging methods in individual differences research, including new data on the role of brain plasticity in cognitive function. The possibility of a unified theory of individual differences in cognitive ability and the extent to which these variables may account for real-world competencies are emphasized, and commentary chapters offer suggestions for further research priorities. Coverage highlights include: The relationship between cognition and temperamental traits. The development of autobiographical memory. Anxiety and attentional control. The neurophysiology of gender differences in cognitive ability. Intelligence and cognitive control. Individual differences in dual task coordination. The effects of subclinical depression on attention, memory, and reasoning. Mood as a shaper of information. Researchers, clinicians, and graduate students in psychology and cognitive sciences, including clinical psychology and neuropsychology, personality and social psychology, neuroscience, and education, will find the Handbook of Individual Differences in Cognition an expert guide to the field as it currently stands and to its agenda for the future.