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**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.

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 (GĂ¶ttingen)

### 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 |