Generalized Difference Methods for Differential Equations
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Author(s): R. Li, Z Chen and W. Wu
Publisher: Marcel Dekker
ISBN:  0 8247 0330 8
Format: hardback
  442pp
Price: £106.50
Review Date: May 23, 2000
Review: This is a textbook on generalized differential methods (GDM). it provides a comprehensive mathematical theory for elliptic, parabolic and hyperbolic differential equations. It compares the finite difference methods and builds up a case for the superiority of GDM, which has grid flexibility higher, accuracy and maintenance of the mass conservation law. Chapters cover convection-dominated diffusion equations and alternatives schemes including the characteristic difference methods proposed by Douglas and Russel. Case applications of GDM to the computation of compressible and incompressible fluid equations are discussed. One- and two-dimensional second-order linear equations, biharmonic equations, and GDM-based on mixed variational principles are discussed. A discontinuous finite-method to obtain highly accurate upwind schemes is given. There is also a review of Sobolev spaces and the generalized solutions on variational problems and their approximations.