Reset Filters
Branch: 虹口分馆乍浦馆

Cover is for reference only

Linear discrete parabolic problems /

This volume introduces a unified, self-contained study of linear discrete parabolic problems through reducing the starting discrete problem to the Cauchy problem for an evolution equation in discrete time. Accessible to beginning graduate students, the book contains a general stability theory of dis...

Full description

Saved in:
Bibliographic Details
Main Authors: Bakaev, Nikolai Yu. (Author)
Corporate Authors: Elsevier Science & Technology.
Published: Elsevier,
Publisher Address: Amsterdam :
Publication Dates: 2006.
Literature type: eBook
Language: English
Edition: First edition.
Series: North-Holland mathematics studies, 203
Subjects:
Stability.
Runge-Kutta formulas.
Differential equations.
Computer science > Mathematics.
MATHEMATICS > General. > General.
Electronic books.
Online Access: http://www.sciencedirect.com/science/bookseries/03040208/203
Summary: This volume introduces a unified, self-contained study of linear discrete parabolic problems through reducing the starting discrete problem to the Cauchy problem for an evolution equation in discrete time. Accessible to beginning graduate students, the book contains a general stability theory of discrete evolution equations in Banach space and gives applications of this theory to the analysis of various classes of modern discretization methods, among others, Runge-Kutta and linear multistep methods as well as operator splitting methods. Key features: * Presents a unified approach to examining discretization methods for parabolic equations. * Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space. * Deals with both autonomous and non-autonomous equations as well as with equations with memory. * Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods. * Provides comments of results and historical remarks after each chapter. Presents a unified approach to examining discretization methods for parabolic equations. Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space. Deals with both autonomous and non-autonomous equations as well as with equations with memory. Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods as well as certain operator splitting methods are studied in detail. Provides comments of results and historical remarks after each chapter.
Carrier Form: 1 online resource (xv, 286 pages).
Bibliography: Includes bibliographical references (pages 269-283) and index.
ISBN: 9780444521408
0444521402
0080462081
9780080462080
Index Number: QA871
CLC: O175.13
Contents: Preface. -- Part I. EVOLUTION EQUATIONS IN DISCRETE TIME. -- Preliminaries. -- Main Results on Stability. -- Operator Splitting Problems. -- Equations with Memory. -- Part II. RUNGE-KUTTA METHODS. -- Discretization by Runge-Kutta methods. -- Analysis of Stability. -- Convergence Estimates. -- Variable Stepsize Approximations. -- Part III. OTHER DISCRETIZATION METHODS. -- The/theta-method. -- Methods with Splitting Operator. -- Linear Multistep Methods. -- Part IV. INTEGRO-DIFFERENTIAL EQUATIONS UNDER DISCRETIZATION. -- Integro-Differential Equations. -- APPENDIX. -- A Functions of Linear Operators. -- B Cauchy Problems in Banach Space.

Related Book Recommendations