Linear Discrete Parabolic Problems

Nikolai Bakaev

ISBN 10: 0444521402 / ISBN 13: 9780444521408

Published by Elsevier Science & Technology Feb 2006, 2006

About this Item

Neuware - 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.

Seller Inventory # 9780444521408

Bibliographic Details

• Title: Linear Discrete Parabolic Problems
• Publisher: Elsevier Science & Technology Feb 2006
• Publication Date: 2006
• Language: English
• ISBN 10: 0444521402
• ISBN 13: 9780444521408
• Binding: Buch
• Condition: Neu
• Dimensions: 234W x 156H x 18D millimeters 234 millimeters width by 156 millimeters height by 18 millimeters depth
• Weight: 603 grams

About this title

Synopsis

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.

Review

"Although this book is dealing only with linear probelms its acheivements are significant also for studying numerical methods for nonlinear parabolic equations. The main topic of the book is focused on problems of discretization abstract parabolic equations but there are also parts for example the problems with memory term and these results can be used also to parabolic partial differential and integro-differential equations."
-ZENTRALBLATT MATH DATABASE, 1931-2007