Finite difference methods in heat transfer.

*(English)*Zbl 0855.65097
Boca Raton, FL: CRC Press. xi, 412 p. (1994).

Above all, this book is an elementary text, an introduction to applications of partial differential equations and numerical methods for approximating their solutions. No theorems or error estimates are presented, and the required mathematical background is minimal.

The book has several attractive features. Foremost, in my opinion, is the large collection of sample problems considered, from elementary diffusion problems up to multidimensional problems in fluid flow, or with phase changes. A reader will understand the origin of a number of such problems, as well as their rotation and background. The book also contains substantial material on computational details, including a chapter on grid generation. It will likely be useful in this regard. Finally, the book is very readable, and contains a number of problems at the end of each chapter.

The book has an obvious weakness; the numerical methods described are largely obsolete. For many or most problems of current interest, involving complex geometry and/or solutions of low regularity, the finite difference methods discussed here are simply not competitive with various projection methods. A reader employing the methods of this book will likely be embarrassed in computational competition, as often occurs on such problems. But he will nonetheless be significantly better prepared for the study of more sophisticated methods.

The book has several attractive features. Foremost, in my opinion, is the large collection of sample problems considered, from elementary diffusion problems up to multidimensional problems in fluid flow, or with phase changes. A reader will understand the origin of a number of such problems, as well as their rotation and background. The book also contains substantial material on computational details, including a chapter on grid generation. It will likely be useful in this regard. Finally, the book is very readable, and contains a number of problems at the end of each chapter.

The book has an obvious weakness; the numerical methods described are largely obsolete. For many or most problems of current interest, involving complex geometry and/or solutions of low regularity, the finite difference methods discussed here are simply not competitive with various projection methods. A reader employing the methods of this book will likely be embarrassed in computational competition, as often occurs on such problems. But he will nonetheless be significantly better prepared for the study of more sophisticated methods.

Reviewer: Michael Sever (Jerusalem)

##### MSC:

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

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

80A20 | Heat and mass transfer, heat flow (MSC2010) |

65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |

35K05 | Heat equation |