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Linear Discrete Parabolic Problems
ID: 173426
Nikolai Bakaev
This volume introduces a unified, self-contained study of linear discrete problem solving problems for an evolution equation in discrete time. Accessible to the beginning of graduate students, the book contains a class of modern discretization methods, among others, Runge-Kutta and linear multistep methods as well as operator splitting methods.
Key features:
* Presents and unified approach to examining discretization methods for parabolic equations.
* Highlights a stability theory in 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 the abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as some 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 in 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 the abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as some operator splitting methods are studied in detail.
· Provides comments of results and historical remarks after each chapter.
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.
173426
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Nikolai Bakaev