The authors approach the problem of solving differential equations using neural networks (NN) including cellular NN. A brief overview of differential equations including considerations regarding numerical methods is given in the first chapter. In the following chapter, a brief history of NN is presented. The next chapters are dedicated to specific aspects regarding the subject of the book. Thus, chapter 3 gives preliminaries on NN starting from definitions and continuing with biological and artificial NN, mathematical models, types of activation function, architectures, various kinds of learning in NN, the multilayer perceptron and, last but not least, NN as universal approximators. The last and largest chapter deals with NN methods for solving differential equations, i.e., the method of multilayer perceptron, the method of radial basis function NN, the method of multiquadric radial basis functions, the method of cellular NN, the method of finite elements NN and wavelet NN. The last part of the chapter contains several workout examples. The book ends with conclusions, an appendix with Matlab codes, a list of 112 references papers and an index. The book is intended to enable the reader to get an image on the variety of NN and the NN methods can be used in solving differential equations. It is a valuable reference material both from the presentation point of view and the provided references.Reviewer: Liviu Goraş (Iaşi)

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