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Numerical methods. Textbook. (Chislennye metody. Uchebnoe posobie.) (Russian. English summary) Zbl 0666.65001

Moskva: Nauka. 432 p.; R. 1.20 (1989).
The contents of this book, written by a leading specialist in the field, A. Samarskiĭ, and his coworker A. Gulin is as follows: Part I. Mathematical simulation and numerical experiment, roundoff errors, second-order difference equations, difference approximations of (ordinary) differential equations (of second order). Part II. Direct and iterative methods for solving systems of linear algebraic equations, interpolation and approximation of functions, numerical integration and differentiation, solution of nonlinear equations and systems of these equations, numerical methods for ordinary differential equations. Part III. The main notions of the theory of difference schemes, the maximum principle and variable dividing for difference schemes, stability theory of difference schemes, direct and iterative methods for grid equations.
The first two parts include introductory and traditional topics of numerical methods and the final part is based on original papers of the authors. The book is well written, and offers an easy access to the basic results. The presentation is systematic, clear for all to read, and can be very useful as a text or for self teaching properties.
Reviewer: J.Albrycht

MSC:

65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65G50 Roundoff error
39A10 Additive difference equations
65Lxx Numerical methods for ordinary differential equations
65F05 Direct numerical methods for linear systems and matrix inversion
65F10 Iterative numerical methods for linear systems
65Dxx Numerical approximation and computational geometry (primarily algorithms)
65Hxx Nonlinear algebraic or transcendental equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
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