Linear Discrete Parabolic Problems, Volume 203
1st Edition
Secure Checkout
Personal information is secured with SSL technology.Free Shipping
Free global shippingNo minimum order.
Table of 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.
Description
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.
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 as well as certain operator splitting methods are studied in detail. ·Provides comments of results and historical remarks after each chapter.
Readership
Experts and beginners in numerical solution of evolution equations. University professors and teachers.
Details
- No. of pages:
- 302
- Language:
- English
- Copyright:
- © North Holland 2006
- Published:
- 2nd December 2005
- Imprint:
- North Holland
- Hardcover ISBN:
- 9780444521408
- eBook ISBN:
- 9780080462080
Reviews
"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
Ratings and Reviews
About the Author
Nikolai Bakaev
Affiliations and Expertise
Russian State Social University, Moscow, Russia
Request Quote
Tax Exemption
Elsevier.com visitor survey
We are always looking for ways to improve customer experience on Elsevier.com.
We would like to ask you for a moment of your time to fill in a short questionnaire, at the end of your visit.
If you decide to participate, a new browser tab will open so you can complete the survey after you have completed your visit to this website.
Thanks in advance for your time.