Periodic Integral and Pseudodifferential Equations with Numerical Approximation PDF Download
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Author: Jukka Saranen
Publisher: Springer
ISBN: 9783662047972
Category : Mathematics
Languages : en
Pages : 452
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Book Description
An attractive book on the intersection of analysis and numerical analysis, deriving classical boundary integral equations arising from the potential theory and acoustics. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.
Author: Jukka Saranen
Publisher: Springer
ISBN: 9783662047972
Category : Mathematics
Languages : en
Pages : 452
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Book Description
An attractive book on the intersection of analysis and numerical analysis, deriving classical boundary integral equations arising from the potential theory and acoustics. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.
Author: Jukka Saranen
Publisher: Springer Science & Business Media
ISBN: 3662047969
Category : Mathematics
Languages : en
Pages : 461
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Book Description
An attractive book on the intersection of analysis and numerical analysis, deriving classical boundary integral equations arising from the potential theory and acoustics. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.
Author: G. Vainikko
Publisher:
ISBN: 9789512231188
Category :
Languages : en
Pages : 108
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Book Description
Author: V. K. Dzyadyk
Publisher: VSP
ISBN: 9789067641944
Category : Mathematics
Languages : en
Pages : 340
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Book Description
This book is the result of 20 years of investigations carried out by the author and his colleagues in order to bring closer and, to a certain extent, synthesize a number of well-known results, ideas and methods from the theory of function approximation, theory of differential and integral equations and numerical analysis. The book opens with an introduction on the theory of function approximation and is followed by a new approach to the Fredholm integral equations to the second kind. Several chapters are devoted to the construction of new methods for the effective approximation of solutions of several important integral, and ordinary and partial differential equations. In addition, new general results on the theory of linear differential equations with one regular singular point, as well as applications of the various new methods are discussed.
Author: M. A. Goldberg
Publisher: Springer Science & Business Media
ISBN: 1475714661
Category : Science
Languages : en
Pages : 351
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Book Description
Author: Madan Mohan Panja
Publisher: CRC Press
ISBN: 0429534280
Category : Mathematics
Languages : en
Pages : 466
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Book Description
Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It’s main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes based on Finite Difference Method, Finite Element Method, Galerkin Method, etc. The objective of this monograph is to deal with numerical techniques to obtain (multiscale) approximate solutions in wavelet basis of different types of integral equations with kernels involving varieties of singularities appearing in the field of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering.
Author: Donald D. James
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 38
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Book Description
Author: Gennadi Vainikko
Publisher: Tartu University Press
ISBN:
Category : Mathematics
Languages : en
Pages : 44
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Book Description
Author: Luigi Rodino
Publisher: Springer Science & Business Media
ISBN: 3764389699
Category : Mathematics
Languages : en
Pages : 337
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Book Description
This volume consists of peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held on August 13-18, 2007, and invited papers by experts in the field.
Author: N. F. Morozov
Publisher: Vieweg+Teubner Verlag
ISBN: 9783663116271
Category : Technology & Engineering
Languages : de
Pages : 375
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Book Description
It was the last book the outstanding mathematician, mechanician and lecturer S. G. Mikhlin took an active part in writing. Having been completed during his lifetime, this book could not be published in Russia due to well know difficulties. Since that time new results in integral equations of elasticity theory have appeared. The works of W. Wendland and his school on numerical methods of solving boundary integral equations, the works of I. Chudinovich on inves tigation of non-stationary integral equations, the works of S. Kuznetsov con nected with the construction of the fundamental solutions for anisotropic me dia and others deserve special mentioning. The authors recognize that though the book is devoted to integral equations of elasticity theory, its contents do not cover all possible directions in this field. So the book does not contain the investigations of pseudo-differential equations of three-dimensional prob lems of elasticity theory, connected with the works of R. Goldstein, I. Klein, G. Eskin; the questions of solving by integral transformations (I. Ufland, L. Slepian, B. Buda. e:v); the theory of symbols of pseudo-differential operators on non-smooth surfaces developed in the works of B. Plamenevski et al. and the new methods of numerical solution of pseudo-differential equations as developed by a school of V. Mazya. The present book gives the classical methods of potential theory in elas ticity and their development and also the solution of a number of problems which here are published in English for the first time.
