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**Nonlinear modelling, tutorial and manual. With an Appendix written by Wolfgang Prager and Jens Schwaiger. With CD-ROM.**
*(English)*
Zbl 1104.65001

The aim of this booklet is to update ideas, algorithms and software on nonlinear modelling; it is a remake and a tribute paid to the author, Günther H. Mehring, by his fellows Peter Schöpf and Jens Schwaiger (Grazer Mathematische Berichte). The book contains a tutorial and a manual for the *NL* software. The tutorial on nonlinear modelling explains the *NL* basic ideas on nonlinear modelling, algorithms, and their correctness. Selected examples, prepared and annotated, support the theory and implementation results. The main fields considered are: evaluating functions, solving differential equations, fitting data, Fourier-analysis, used-defined libraries, statistical reference datasets.

The manual for nonlinear programming describes the main characteristics of the *NL* program package devoted to the analysis of nonlinear models. There are presented the *NL* features, requirements, hands-on instructions for how to apply the *NL* program to specific problems of nonlinear modeling: numerics, equation systems, parameters, the *NL* output etc. Computational methods (integration and Fourier coefficients, statistics, multivariate models) are outlined. The appendix shows (with enclosed screenshots) how the *NL* program can be used step-by-step. The attached CD contains the software and the original plain text files on which the book contents was developed.

The manual for nonlinear programming describes the main characteristics of the *NL* program package devoted to the analysis of nonlinear models. There are presented the *NL* features, requirements, hands-on instructions for how to apply the *NL* program to specific problems of nonlinear modeling: numerics, equation systems, parameters, the *NL* output etc. Computational methods (integration and Fourier coefficients, statistics, multivariate models) are outlined. The appendix shows (with enclosed screenshots) how the *NL* program can be used step-by-step. The attached CD contains the software and the original plain text files on which the book contents was developed.

Reviewer: Neculai Curteanu (Iaşi)

### MSC:

65-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis |

90C30 | Nonlinear programming |

00A71 | General theory of mathematical modeling |

65Y15 | Packaged methods for numerical algorithms |

65L05 | Numerical methods for initial value problems involving ordinary differential equations |

65D10 | Numerical smoothing, curve fitting |

65T40 | Numerical methods for trigonometric approximation and interpolation |

65C60 | Computational problems in statistics (MSC2010) |

65K05 | Numerical mathematical programming methods |