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Analytical and numerical methods for Volterra equations. (English) Zbl 0566.65094
SIAM Studies in Applied Mathematics, 7. Philadelphia: SIAM - Society for Industrial and Applied Mathematics. (Distr. by John Wiley & Sons). XIII, 227 p. £28.25 (1985).
This is a good, concise introduction into the analytical and numerical solution of Volterra integral and integrodifferential equations, written by one of the early workers in the field. As a general characteristic of the book one could say that it provides insight through the detailed treatment of the simplest methods. A number of exercises woven throughout the text enables and urges the reader to work out and check many unproved statements. The first half of the book treats the theory of Volterra integral equations of the second and the first kind and it includes a chapter which describes some applications. The second part treats numerical methods for general second and first kind Volterra integral equations and for Volterra integrodifferential equations, and product integration methods for (weakly) singular Volterra integral equations of the second and the first kind. The book concludes with a short chapter giving four PASCAL procedures for solving Volterra equations, and a chapter with three interesting ”case studies”, motivated by the fact that in practical situations difficulties may arise which usually are not handled by the general theory. A list of 249 references has been added, of which only a small portion has actually been discussed in the text. A supplementary list mentions 35 recent papers from the period 1982-1984 which, however, are neither discussed nor referred to in the text at all.
Reviewer: H.J.J.te Riele

MSC:
65R20 Numerical methods for integral equations
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
45D05 Volterra integral equations
45-02 Research exposition (monographs, survey articles) pertaining to integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
45J05 Integro-ordinary differential equations
45-04 Software, source code, etc. for problems pertaining to integral equations