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Analyse numérique des équations différentielles. (Numerical analysis of differential equations). (French) Zbl 0635.65079
Collection Mathématique Appliquées pour la Maîtrise. Paris etc.: Masson. VIII, 171 p.; FF 98.00 (1984).
We propose to give a description and an analysis of the principal modern methods used in the numerical solution of the Cauchy problem. We have sought both to give a precise mathematical context for the problem and its solution methods and to avoid the overly technical aspects of the material. We limit ourselves to describing the algorithms only in a general form, and the proofs call upon simple mathematical tools: error bounds, convergence results, stability results, etc. This text is addressed to undergraduate and graduate students and to engineers, economists and others who use numerical analysis of differential equations.

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A30 Linear ordinary differential equations and systems
34A34 Nonlinear ordinary differential equations and systems
00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)
41A40 Saturation in approximation theory
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures