Hypersingular Integral Equations And Their Applications
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Hypersingular Integral Equations and Their Applications
Author | : I.K. Lifanov,L.N. Poltavskii,MG.M. Vainikko |
Publsiher | : CRC Press |
Total Pages | : 416 |
Release | : 2003-12-29 |
Genre | : Mathematics |
ISBN | : 9780203402160 |
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A number of new methods for solving singular and hypersingular integral equations have emerged in recent years. This volume presents some of these new methods along with classical exact, approximate, and numerical methods. The authors explore the analysis of hypersingular integral equations based on the theory of pseudodifferential operators and co
Hypersingular Integrals and Their Applications
Author | : Stefan Samko |
Publsiher | : CRC Press |
Total Pages | : 382 |
Release | : 2001-10-25 |
Genre | : Mathematics |
ISBN | : 0415272688 |
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Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences. This volume develops these approaches in a comprehensive treatment of hypersingular integrals and their applications. The author is a renowned expert on the topic. He explains the basics before building more sophisticated ideas, and his discussions include a description of hypersingular integrals as they relate to functional spaces. Hypersingular Integrals and Their Applications also presents recent results and applications that will prove valuable to graduate students and researchers working in mathematical analysis.
Applied Singular Integral Equations
Author | : B. N. Mandal,A. Chakrabarti |
Publsiher | : CRC Press |
Total Pages | : 270 |
Release | : 2016-04-19 |
Genre | : Mathematics |
ISBN | : 9781439876213 |
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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.
Topics in Integral and Integro Differential Equations
Author | : Harendra Singh,Hemen Dutta,Marcelo M. Cavalcanti |
Publsiher | : Springer Nature |
Total Pages | : 255 |
Release | : 2021-04-16 |
Genre | : Technology & Engineering |
ISBN | : 9783030655099 |
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This book includes different topics associated with integral and integro-differential equations and their relevance and significance in various scientific areas of study and research. Integral and integro-differential equations are capable of modelling many situations from science and engineering. Readers should find several useful and advanced methods for solving various types of integral and integro-differential equations in this book. The book is useful for graduate students, Ph.D. students, researchers and educators interested in mathematical modelling, applied mathematics, applied sciences, engineering, etc. Key Features • New and advanced methods for solving integral and integro-differential equations • Contains comparison of various methods for accuracy • Demonstrates the applicability of integral and integro-differential equations in other scientific areas • Examines qualitative as well as quantitative properties of solutions of various types of integral and integro-differential equations
Singular Integral Equations
Author | : N. I. Muskhelishvili,J. R. M. Radok |
Publsiher | : Courier Corporation |
Total Pages | : 466 |
Release | : 2008-01-01 |
Genre | : Science |
ISBN | : 9780486462424 |
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This high-level treatment considers one-dimensional singular integral equations involving Cauchy principal values, covering Hölder condition, Hilbert and Riemann-Hilbert problems, Dirichlet problems, inversion formulas for arcs, more. 1992 edition.
Wavelet Based Approximation Schemes for Singular Integral Equations
Author | : Madan Mohan Panja,Birendra Nath Mandal |
Publsiher | : CRC Press |
Total Pages | : 466 |
Release | : 2020-06-07 |
Genre | : Mathematics |
ISBN | : 9780429534287 |
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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.
Handbook of Integral Equations
Author | : Andrei D. Polyanin,Alexander V. Manzhirov |
Publsiher | : CRC Press |
Total Pages | : 1143 |
Release | : 2008-02-12 |
Genre | : Mathematics |
ISBN | : 9780203881057 |
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Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa
Integral Equations and Their Applications
Author | : Matiur Rahman |
Publsiher | : WIT Press |
Total Pages | : 385 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 9781845641016 |
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The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's function as a symmetric kernel of the integral equations.