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.
Author(s): Nikolai Yu. Bakaev (Eds.)
Series: North-Holland mathematics studies 203
Edition: 1st ed
Publisher: Elsevier
Year: 2006
Language: English
Pages: 3-286
City: Amsterdam; Boston
Tags: Математика;Вычислительная математика;
Content:
Preface
Pages v-xii
Chapter 1 Preliminaries Original Research Article
Pages 3-19
Chapter 2 Main results on stability Original Research Article
Pages 21-52
Chapter 3 Operator splitting problems Original Research Article
Pages 53-69
Chapter 4 Equations with memory Original Research Article
Pages 71-79
Chapter 5 Discretization by Runge-Kutta methods Original Research Article
Pages 83-110
Chapter 6 Analysis of Stability Original Research Article
Pages 111-146
Chapter 7 Convergence estimates Original Research Article
Pages 147-178
Chapter 8 Variable stepsize approximations Original Research Article
Pages 179-205
Chapter 9 The θ-Method Original Research Article
Pages 211-217
Chapter 10 Methods with splitting operator Original Research Article
Pages 219-225
Chapter 11 Linear multistep methods Original Research Article
Pages 227-242
Chapter 12 Integro-Differential equations under discretization Original Research Article
Pages 247-253
Appendix A Functions of linear operators Original Research Article
Pages 255-263
Appendix B Linear cauchy problems in banach space Original Research Article
Pages 265-267
Bibliography
Pages 269-283
Index
Pages 284-286
