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.


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