Review of the book by Piotr Krzyżanowski: ,,Scientific and Engineering Computations - Fast, Reliable and Effective''

Abstract

Scientific computation is at present one of the most efficient approaches available to researchers and developers for applied mathematics, technical, economical and natural sciences. This book provides practical guidance on how to perform numerical computer simulations using advanced computational and visualization software tools, and the book in particular caters for nonspecialists in this area seeking to utilize such approaches in their work. The book leads the reader step by step through different types of realization of computational tasks, with an increasing degree of depth. Initially MATLAB and Octave software packages are covered, followed by numerical libraries (for example BLAS and LAPACK), methods for optimizing the numerical programs in C and finally visualization packages. Catering for different levels of expertise and covering the most important tools, the book allows the reader to select and learn approaches suitable for their situation and computational task. Throughout there is a rich variety of well selected examples, exercises, source codes, pictures, diagrams and tables collating the experimental results. For example, the reader is familiarized with some numerical applications of solving ordinary and partial differential equations (ODEs or PDEs). In section 7.9.2 the equation of the van der Pola, which appears in the analysis of simple electrical circuits, is discussed. The programming script solving the equation in question is given and important pertinent details are given. Difficulties with the stability of the solution for ODE is on the other hand discussed for the specific Lorentz equation in the following section, 7.9.3., and likewise the pertinent programming script solving the Lorentz system is provided. Then in section 7.10 some numerical examples for solving PDEs are discussed. The classical equation of diffusion over a rectangle is here considered. All important issues related to discretization and the corresponding numerical schemes are covered for this particular type of equation. In summary, this book is particularly recommended to the nonspecialists, as it offers an attractive and soft entrance into the delicate matter of complicated scientific computation. The examples presented in the book are chosen carefully, and the exercises are stimulating, and help the reader gather the author’s expertise. This book should make resolution of computational problems both easier and enjoyable.