Modelling mathematical methods and scientific computation.

*(English)*Zbl 0871.65001
CRC Mathematical Modelling Series. Boca Raton, FL: CRC Press. xiv, 497 p. with disc. (1995).

The aim of this first volume of a series devoted to mathematical modelling in applied science is to present the theory of mathematical modelling by the equations of classical mathematical analysis. The authors’ proposal is essentially founded on the idea that mathematical methods suitable to solve mathematical problems cannot be separated from the various aspects of mathematical modelling.

The topics of the book include: mathematical modelling, discrete models, continuous models, inverse and stochastic problems. The preface provides a preliminary description of the main features of mathematical modelling as a science. The first chapter treats the general framework needed by mathematical modelling: definitions, classifications, general modelling procedures, and validation methods. The second chapter deals with the analysis of discrete models: modelling methods and related mathematical methods. The relevant content of this chapter is the analysis of models defined in terms of ordinary differential equations. The third chapter deals with the analysis of continuous models, and, in particular, with models defined in terms of partial differential equations. The fourth chapter treats the inverse problem and stochastic modelling. Some information is given about the problem solutions, being directly obtained by measurements on the real physical systems.

The book is proposed as a dedicated textbook for higher courses of mathematics referred to as master courses in technological and applied sciences. The writing style is concise. Use of remarks is frequently made in order to print out crucial aspects, and useful mathematical methods are reported in the appendices at the end of the book. Most of the attention is addressed to the applications. Some problems are proposed with reference to the contents of the chapters. The book provides, at the end of each chapter, some scientific programs related to the solution of sample problems (a diskette delivered with the book contains all these programs).

The topics of the book include: mathematical modelling, discrete models, continuous models, inverse and stochastic problems. The preface provides a preliminary description of the main features of mathematical modelling as a science. The first chapter treats the general framework needed by mathematical modelling: definitions, classifications, general modelling procedures, and validation methods. The second chapter deals with the analysis of discrete models: modelling methods and related mathematical methods. The relevant content of this chapter is the analysis of models defined in terms of ordinary differential equations. The third chapter deals with the analysis of continuous models, and, in particular, with models defined in terms of partial differential equations. The fourth chapter treats the inverse problem and stochastic modelling. Some information is given about the problem solutions, being directly obtained by measurements on the real physical systems.

The book is proposed as a dedicated textbook for higher courses of mathematics referred to as master courses in technological and applied sciences. The writing style is concise. Use of remarks is frequently made in order to print out crucial aspects, and useful mathematical methods are reported in the appendices at the end of the book. Most of the attention is addressed to the applications. Some problems are proposed with reference to the contents of the chapters. The book provides, at the end of each chapter, some scientific programs related to the solution of sample problems (a diskette delivered with the book contains all these programs).

Reviewer: D.Petcu (Timişoara)

##### MSC:

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

65Lxx | Numerical methods for ordinary differential equations |

65Nxx | Numerical methods for partial differential equations, boundary value problems |

00A71 | General theory of mathematical modeling |

65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |

65C99 | Probabilistic methods, stochastic differential equations |