Approximate solutions of operator Equalions

Mingjltn Book Reviews, Zhongying Ciien, Guanrong Ciien, Chen
1998 World Scientifìc   unpublished
Singapore-London;Hong Kong, I 997, xiii+344 pp" ISBN 98 t-02-3064-8' The book is an interesting introduction to approximate solutions of operator equations in Banach spaces ofreal or complex functions, This abstract approach enables the authols to tfeat' from a unifling point of view, various kinds of linear and nonlinear, ordinary and partial differential' integri Jr integro-differential and functional evolution equâtions formulated in elementary or abstract f,rnction spaces, with initial
more » ... , with initial boundary value conditions and possible additional constraints' The book is designed as an elementary and self-contained introduction to some impofant notions such as computational schemes, convefgence analysis, stabitity conditions and error estimates' The volume is divided into six chapters and two appendices' Chapter |-Introductior-is an overview ofthe projection approximation lechniques-projection operators; projective approximation scheme. The approximate solutions of operatol equations in Banach or Hilbert space setting are discussed in Chapter 2 for compact linear operators and in Chapter 3 for other linear operators (including densely defined operators)' Applications to Fredholm integral equations and to bormdary value problems for ordinary and partial differential equations aee includedr Topologicaldegreeandfixedpointtheorems,comprisingapproximatesolutionsofnonlinear fixed point equations, are discussed in the fourth chapter' chapter 5 deals with monotone and K-monotone nonlinear operatot equations and their approúmate solutions. Perturbed equations together with some applications to typical nonlinear differerrtial equations are included, too' The final chapter is concerned with operator evolution equations and their projective approximate solution. Continuous-time and discrete-time projection methods for first and second order abstract evolution equations are considered' Two appendices, one on frrndamental results ftom ñurctional analysis and the other on sobolev