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The numerical solution of ordinary and partial differential equations. (English) Zbl 0657.65003
Boston, MA: Academic Press, Inc. xii, 271 p. $ 39.95 (1988).
The aim of the book is to give a solid introduction to the computer solution of ordinary and partial differential equations, appropriate for a senior level undergraduate or first year graduate course.
In chapter 0, a review of direct methods for the solution of linear systems is given. The emphasis is on the special features of the systems that arise during the solution of differential equations. Chapters 1 to 4 deal with the more commonly used finite difference methods for solving initial value problems of ordinary differential equations, the initial value diffusion problem, initial value transport and wave problems and boundary value problems. Both one-dimensional and multidimensional problems are discussed.
The finite difference methods discussed in chapters 2-4 are mostly classical low order formulas, easy to program but not ideal for problems with poorly behaved solutions or for problems in irregular multidimensional regions. More complicated finite difference techniques are not studied in this book. Chapter 5 contains an overview of the basic ideas behind the finite element method. There are two appendices: - the first on the Fourier stability method and the second on parallel algorithms.
Throughout the book FORTRAN 77 programs are given for the problems solved. The book is a useful text for students as well as teachers.
Reviewer: K.T.S.R.Iyengar

MSC:
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65Lxx Numerical methods for ordinary differential equations
65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65Nxx Numerical methods for partial differential equations, boundary value problems
65F05 Direct numerical methods for linear systems and matrix inversion
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
35-04 Software, source code, etc. for problems pertaining to partial differential equations
65Y05 Parallel numerical computation
Software:
PDE2D
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