Numerical Methods in Engineering and Science

Abstract: with partial differential equations. The governing equations are developed in the context of a physical model and both analytical and numerical methods to solve the problem are explained. The first two chapters serve as introductory material for the subject treated in the book. In Chapter 1 the different difference approximations for derivatives are introduced. The important concepts in finite difference methods, such as error analysis and stability are treated well. Efforts have been made to distinguish between implicit and explicit methods in solving problems. In Chapter 2 the author discusses methods of solution for the first order partial differential equations. The method of characteristics is introduced and the applications of difference methods are reviewed. Chapter 3 forms a major part of the book, gives a thorough treatment to the development of second order hyperbolic partial differential equations and various analytical methods for solving them. The concepts of domains of influence and dependence are explained well. The author has also dealt with conservation laws and propagation of discontinuities in the context of the wave equation. The latter part of this chapter contains several examples dealing with the application of difference methods in solving both linear and nonlinear wave propagation problems. In Chapter 4 parabolic equations have received only a cursory treatment in comparison to the hyperbolic system in the previous chapter. In the context of heat conduction both implicit and explicit difference methods for solving the problems are illustrated. Stability analysis has been carried out for the difference schemes discussed in Chapters 3 and 4. Chapter 5 deals with analytical treatment of the governing equations in fluid dynamics. Though the subject has been dealt with in some detail, it does not contain any description of difference methods for dealing with shocks or other fluid dynamics problems. The exercises at the end of the chapters places emphasis on analytical methods. The inclusion of a list of references for further study would have been useful to motivated readers to further their knowledge in this field. A nice feature of this book is that it gives a good blend of analytical and numerical methods for solving problems. This book could serve as an introductory text to students in engineering sciences and as a guide to practicing engineers to acquaint them with difference methods for solving transient problems.