Random differential equations in scientific computing.

*(English)*Zbl 1323.60002
London: Versita (ISBN 978-83-7656-025-0/hbk; 978-83-7656-024-3/pbk; 978-83-7656-026-7/ebook). xxii, 624 p. (2013).

Proceeding from a problem-centred point of view, the authors present a detailed treatment of random differential equations, considering both the analysis and the numerics thereof. Both dynamical systems and scientific computing are constantly in view, and heavy use is made of MATLAB.

In Part I, we find an introduction to the modelling of randomly perturbed phenomena, the pertinent random partial differential equations being reduced to random ordinary differential equations. Foundations of ordinary differential equations and their role in the relationship between dynamical systems and scientific computing are discussed in Part II, while the third part deals with important aspects (e.g., fast Fourier transforms and space-filling curves) in scientific computing. A deeper study of random differential equations is undertaken in Part IV, while the fifth part contains a useful illustration of the material in the book by way of details of the workshop, given by the authors, on which the present work is based.

This text will no doubt be of value to those who use scientific computing ‘in practice’, and the authors are to be congratulated on the amount of work they have clearly put into it.

However, there are several aspects that detract from the merit of the work, some of which could have been overcome by careful editing. One matter is the printing of the Index before the Bibliography, while another is the use of the word ‘seminary’ for ‘seminar’ on page iii, and ‘Poission’ for ‘Poisson’ on page 579. The printing in some of the figures is smaller than I personally would have liked.

I am more worried by the fact that, on page 85, Example 3.1 opens with the words ‘Following [207], p. 467’, and what follows is a direct copy of a paragraph from the cited reference. Despite the authors’ use of the word ‘Following’, the absence of quotation marks does not make it obvious that a quotation is intended. More diligence in the editing process would remove such misleading impressions.

In Part I, we find an introduction to the modelling of randomly perturbed phenomena, the pertinent random partial differential equations being reduced to random ordinary differential equations. Foundations of ordinary differential equations and their role in the relationship between dynamical systems and scientific computing are discussed in Part II, while the third part deals with important aspects (e.g., fast Fourier transforms and space-filling curves) in scientific computing. A deeper study of random differential equations is undertaken in Part IV, while the fifth part contains a useful illustration of the material in the book by way of details of the workshop, given by the authors, on which the present work is based.

This text will no doubt be of value to those who use scientific computing ‘in practice’, and the authors are to be congratulated on the amount of work they have clearly put into it.

However, there are several aspects that detract from the merit of the work, some of which could have been overcome by careful editing. One matter is the printing of the Index before the Bibliography, while another is the use of the word ‘seminary’ for ‘seminar’ on page iii, and ‘Poission’ for ‘Poisson’ on page 579. The printing in some of the figures is smaller than I personally would have liked.

I am more worried by the fact that, on page 85, Example 3.1 opens with the words ‘Following [207], p. 467’, and what follows is a direct copy of a paragraph from the cited reference. Despite the authors’ use of the word ‘Following’, the absence of quotation marks does not make it obvious that a quotation is intended. More diligence in the editing process would remove such misleading impressions.

Reviewer: Andrew Dale (Durban)

##### MSC:

60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |

60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |

65C30 | Numerical solutions to stochastic differential and integral equations |