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Numerical solution of partial differential equations. Finite difference methods. 3rd ed. (English) Zbl 0576.65089

Oxford Applied Mathematics and Computing Science Series. Oxford: Clarendon Press. XIII, 337 p. hbk: £20.00; pbk: £10.95 (1985).
The new edition is a revision of the second edition (1978; Zbl 0389.65040) which was a revision of the first edition (1965; Zbl 0123.118). Chapters 2 and 3 have been recast and partly rewritten. Chapter 2 is now a treatment of convergence and stability of finite difference methods for parabolic equations. Chapter 3 has some new material on reduction to a system of ordinary differential equations, PadĂ© approximations to the exponential and extrapolation in time to improve accuracy. Chapter 4 on hyperbolic equations is expanded to include applications of the new material in chapter 3. Chapter 5 has a slightly changed presentation of SOR. The changes are all improvements. Chapter 2 still has its tables of numbers, although the ease of obtaining graphical output nowadays makes them appear slightly old fashioned. The use of spectral radius of the finite difference matrix to determine stability could be accompanied by some explanation of why it is not always sufficient. The new material in chapter 3 is interesting and worthwhile. The book has lasted well and the new edition gives it a fresh lease of life. It remains a good introduction and happily still looks like a book and not a photocopy.
Reviewer: J.D.P.Donnelly

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65F10 Iterative numerical methods for linear systems
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35K05 Heat equation
35L05 Wave equation