Preface

This volume is an introduction to topics of numerical analysis frequently used in the nuclear reactor field. Numerical methods are very much more powerful than analytical ones in finding solutions to the specific, exceedingly complex problems which arise as a result of the complicated dependence of nuclear cross sections upon energy and the very intricate geometries so often found in nuclear reactors. These difficulties confronting the nuclear engineer are aggravated by the demand for safety of a very high order and the need for accuracy. Therefore numerical methods employed in the design and analysis of nuclear reactors require the use of computers for their solution. In addition, most nuclear reactor problems involve many dimensions. For this reason and because of their great flexibility, digital computers have been used almost exclusively in the nuclear reactor field, except for problems involving control. Consequently, training in the use of computers and the numerical methods pertinent to the reactor field is required of every serious nuclear engineer. With these thoughts in mind, we have written a text to introduce students to the methods by which machine calculations are performed on practical problems in the reactor field, with emphasis on those methods specific to the field. A number of special numerical methods for the treatment of neutron and gamma-ray transport problems have evolved. These were taught for three years as part of courses that also included analytical methods. It was realized that the material in numerical analysis could be taught to those with far less preparation in mathematics by the addition of certain introductory material and that, further, the need and interest in training in numerical methods was much broader than that in analytical methods. Accordingly, the methods special to reactor analysis are presented in the last three chapters of this book. The preparatory subjects appear in the first three chapters; these are very useful to the nuclear engineer in their own right. It has been our experience in some five years of teaching the material as presently organized that it can be assimilated in one term in some forty or so lectures by students at the graduate level who have had a basic course in differ­ ential equations and an introductory course in reactor physics. Thus, first and second year graduate students can use this book. We have found that most students digest new subjects properly only by working problems. Accordingly,