Thomas, J. W. Numerical partial differential equations: Finite difference methods. (English) Zbl 0831.65087 Texts in Applied Mathematics. 22. New York, NY: Springer-Verlag. xv, 445 p. (1995). The present textbook is the first part of a two-volume work on numerical methods for partial differential equations (PDEs), the second volume of which has yet to be published in the same series. The first volume is an introductory text to techniques, analysis and algorithms of finite difference schemes for PDEs.After an introductory first chapter in which the use of finite differences as approximate derivatives is explained and motivated, the important notions of consistency, stability and convergence of finite difference approximations is discussed in chapters 2 and 3. Computational interludes conclude both chapters to provide numerical examples.In chapters 4 and 5 discretisations of parabolic and hyperbolic equations are discussed in detail. Chapter 6 is devoted to systems of partial differential equations and their finite difference analogons. A chapter on dispersion and dissipation concludes this volume.Computational interludes are given at the end of nearly all chapters and algorithmic details are described throughout the book. Reviewer: Th.Sonar (Göttingen) Cited in 2 ReviewsCited in 279 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 62-02 Research exposition (monographs, survey articles) pertaining to statistics 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35K15 Initial value problems for second-order parabolic equations 35L15 Initial value problems for second-order hyperbolic equations Keywords:textbook; algorithms; finite difference schemes; consistency; stability; convergence; numerical examples; parabolic and hyperbolic equations PDFBibTeX XMLCite \textit{J. W. Thomas}, Numerical partial differential equations: Finite difference methods. New York, NY: Springer-Verlag (1995; Zbl 0831.65087)