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ISBN: 9780511543234 9780521806152 9780511265884 0511265883 0511263619 9780511263613 0511265166 9780511265167 0511543239 0521806151 1107158818 1280749911 9786610749911 0511317557 0511264429 9781107158818 9781280749919 6610749914 9780511317552 9780511264429 Year: 2004 Publisher: Cambridge : Cambridge University Press,
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Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory terms, delay equations, and differential-algebraic and integral-algebraic equations. Each chapter starts with a self-contained introduction to the relevant theory of the class of equations under consideration. Numerous exercises and examples are supplied, along with extensive historical and bibliographical notes utilising the vast annotated reference list of over 1300 items. In sum, Hermann Brunner has written a treatise that can serve as an introduction for students, a guide for users, and a comprehensive resource for experts.
Collocation methods --- Volterra equations --- 519.64 --- 681.3*G19 --- Numerical analysis --- Differential equations --- Integral equations --- 681.3*G19 Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) --- Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) --- 519.64 Numerical methods for solution of integral equations. Quadrature formulae --- Numerical methods for solution of integral equations. Quadrature formulae --- Numerical solutions --- Collocation methods. --- Numerical solutions.
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ISBN: 1316981541 1316984133 1316162494 Year: 2017 Publisher: Cambridge : Cambridge University Press,
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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.
Integral equations. --- Volterra equations --- Functional analysis. --- Numerical solutions.
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Year: 2000 Publisher: Wien Osterreichische Akademie der Wissenschaften
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Year: 1987 Publisher: Basel : Karger,
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Year: 1925 Publisher: Marburg N.G. Elwert
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Year: 1975 Publisher: München Bayerische Verwaltung der staatlichen Schlösser, Gärten und Seen
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Year: 1967 Publisher: München Bayerische Verwaltung der staatlichen Schlösser, Gärten und Seen
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Year: 1901 Publisher: Bruxelles s.n.
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Year: 1885 Publisher: Berlin [Verlag nicht ermittelbar]
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Year: 1967 Publisher: Gärten und Seen: Bayerische Verwaltung der staatlichen Schlösser, Gärten und Seen,
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