Multidimensional Weakly Singular Integral Equations

Multidimensional Weakly Singular Integral Equations PDF

Author: Gennadi Vainikko

Publisher: Springer

Published: 2006-11-15

Total Pages: 169

ISBN-13: 354047773X

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The final aim of the book is to construct effective discretization methods to solve multidimensional weakly singular integral equations of the second kind on a region of Rn e.g. equations arising in the radiation transfer theory. To this end, the smoothness of the solution is examined proposing sharp estimates of the growth of the derivatives of the solution near the boundary G. The superconvergence effect of collocation methods at the collocation points is established. This is a book for graduate students and researchers in the fields of analysis, integral equations, mathematical physics and numerical methods. No special knowledge beyond standard undergraduate courses is assumed.

Multidimensional Singular Integrals and Integral Equations

Multidimensional Singular Integrals and Integral Equations PDF

Author: S. G. Mikhlin

Publisher: Elsevier

Published: 2014-07-10

Total Pages: 273

ISBN-13: 1483164497

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Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.

Singular Integral Equations

Singular Integral Equations PDF

Author: E.G. Ladopoulos

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 569

ISBN-13: 3662042916

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The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

Applied Singular Integral Equations

Applied Singular Integral Equations PDF

Author: B. N. Mandal

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 274

ISBN-13: 1439876215

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The book is devoted to varieties of linear singular integral equations, with special emphasis on their methods of solution. It introduces the singular integral equations and their applications to researchers as well as graduate students of this fascinating and growing branch of applied mathematics.

From Divergent Power Series to Analytic Functions

From Divergent Power Series to Analytic Functions PDF

Author: Werner Balser

Publisher: Springer

Published: 1994-08-29

Total Pages: 124

ISBN-13: 9783540582687

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Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.

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