Stability of the Spline Collocation Method for Volterra Integro-differential Equations PDF Download
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Author: Mare Tarang
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 98
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Book Description
Author: Mare Tarang
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 98
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Book Description
Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 9780521806152
Category : Mathematics
Languages : en
Pages : 620
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Book Description
Publisher Description
Author: Hermann Brunner
Publisher: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 608
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Book Description
This monograph presents the theory and modern numerical analysis of Volterra integral and integro-differential equations, including equations with weakly singular kernels. While the research worker will find an up-to-date account of recent developments of numerical methods for such equations, including an extensive bibliography, the authors have tried to make the book accessible to the non-specialist possessing only a limited knowledge of numerical analysis. After an introduction to the theory of Volterra equations and to numerical integration, the book covers linear methods and Runge-Kutta methods, collocation methods based on polynomial spline functions, stability of numerical methods, and it surveys computer programs for Volterra integral and integro-differential equations.
Author: H. Brunner
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
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Book Description
Author: Peter Linz
Publisher: SIAM
ISBN: 0898711983
Category : Mathematics
Languages : en
Pages : 228
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Book Description
Presents integral equations methods for the solution of Volterra equations for those who need to solve real-world problems.
Author: Serge Dubuc
Publisher: American Mathematical Soc.
ISBN: 9780821870181
Category : Mathematics
Languages : en
Pages : 412
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Book Description
This work is based on a series of thematic workshops on the theory of wavelets and the theory of splines. Important applications are included. The volume is divided into four parts: Spline Functions, Theory of Wavelets, Wavelets in Physics, and Splines and Wavelets in Statistics. Part one presents the broad spectrum of current research in the theory and applications of spline functions. Theory ranges from classical univariate spline approximation to an abstract framework for multivariate spline interpolation. Applications include scattered-data interpolation, differential equations and various techniques in CAGD. Part two considers two developments in subdivision schemes; one for uniform regularity and the other for irregular situations. The latter includes construction of multidimensional wavelet bases and determination of bases with a given time frequency localization. In part three, the multifractal formalism is extended to fractal functions involving oscillating singularites. There is a review of a method of quantization of classical systems based on the theory of coherent states. Wavelets are applied in the domains of atomic, molecular and condensed-matter physics. In part four, ways in which wavelets can be used to solve important function estimation problems in statistics are shown. Different wavelet estimators are proposed in the following distinct cases: functions with discontinuities, errors that are no longer Gaussian, wavelet estimation with robustness, and error distribution that is no longer stationary. Some of the contributions in this volume are current research results not previously available in monograph form. The volume features many applications and interesting new theoretical developments. Readers will find powerful methods for studying irregularities in mathematics, physics, and statistics.
Author: Gheorghe Micula
Publisher: Springer Science & Business Media
ISBN: 9401153388
Category : Mathematics
Languages : en
Pages : 622
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Book Description
The purpose of this book is to give a comprehensive introduction to the theory of spline functions, together with some applications to various fields, emphasizing the significance of the relationship between the general theory and its applications. At the same time, the goal of the book is also to provide new ma terial on spline function theory, as well as a fresh look at old results, being written for people interested in research, as well as for those who are interested in applications. The theory of spline functions and their applications is a relatively recent field of applied mathematics. In the last 50 years, spline function theory has undergone a won derful development with many new directions appearing during this time. This book has its origins in the wish to adequately describe this development from the notion of 'spline' introduced by 1. J. Schoenberg (1901-1990) in 1946, to the newest recent theories of 'spline wavelets' or 'spline fractals'. Isolated facts about the functions now called 'splines' can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J.
Author: Maria Rosaria Crisci
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 1316982653
Category : Mathematics
Languages : en
Pages : 405
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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.
Author: Jean-Paul Kauthen
Publisher:
ISBN:
Category : Collocation methods
Languages : en
Pages : 226
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Book Description
