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    Izzo, G. Messina, E. and Vecchio, A. 2018. Stability of Numerical Solutions for Abel–Volterra Integral Equations of the Second Kind. Mediterranean Journal of Mathematics, Vol. 15, Issue. 3,

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    Solodusha, S. V. 2018. Numerical Solution of A Class of Systems of Volterra Polynomial Equations of the First Kind. Numerical Analysis and Applications, Vol. 11, Issue. 1, p. 89.

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Book description

This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a 'stepping stone' to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.

Reviews

'One of the strengths of the book is the attention given to the history of the subject and the large number of references to older literature. At the same time the author succeeds in giving an introduction to the current state of the art in the theory of Volterra integral equations and the notes at the end of each chapter are very helpful in this respect as they point the reader to the relevant papers.'

Gustaf Gripenberg Source: Zentralblatt MATH

'In summary, the book is a very clear and thorough presentation of the theory. It is an excellent compendium and text with a simple exposition and few lengthy proofs. It is very thoroughly referenced (with 39 pages of references), with most of the references explained or commented on in the text. The audience will include students for a specialized course and researchers. … I highly recommend the book.'

John A. DeSanto Source: Mathematical Reviews

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