##
**Theory of difference equations: numerical methods and applications.
2nd ed.**
*(English)*
Zbl 1014.39001

Pure and Applied Mathematics, Marcel Dekker. 251. New York NY: Marcel Dekker. x, 300 p. (2002).

In this second edition [for a review of the first one (1988) see Zbl 0683.39001], the contents have been revised throughout. Chapter one and three have been expanded while chapter five and nine are new. In chapter five, several examples involve tridiagonal matrices via boundary value problems. The invertibility of the matrices is studied. Another section describes a reduction method via LU factorization. The initial difference equation is represented in matrix form \(M_0g=d\) with \(M_0\) tridiagonal. The case when \(M_0\) is Toeplitz is examined further. Chapter nine presents the role of difference equations in historically relevant problems (iteration of mean type operations, root finding of polynomials in an iterative way, an example of a difference equation whose solution is the set of Fermat numbers).

Reviewer: A.Akutowicz (Berlin)

### MSC:

39A05 | General theory of difference equations |

39A11 | Stability of difference equations (MSC2000) |

65Q05 | Numerical methods for functional equations (MSC2000) |

65N06 | Finite difference methods for boundary value problems involving PDEs |

93C55 | Discrete-time control/observation systems |

92D25 | Population dynamics (general) |

39-02 | Research exposition (monographs, survey articles) pertaining to difference and functional equations |