Wavelet Based Approximation Schemes for Singular Integral Equations: 1st Edition (Hardback) book cover

Wavelet Based Approximation Schemes for Singular Integral Equations

1st Edition

By Madan Mohan Panja, Birendra Nath Mandal

CRC Press

325 pages | 50 B/W Illus.

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Hardback: 9780367199173
pub: 2020-01-01
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Description

Wavelet Based Approximation Schemes for Singular Integral Equations discusses the numerical techniques for getting multiscale solutions of different types of integral equations with kernels involving various singularities appearing in the fields of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering. The numerical methods of wavelet bases (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes that are based on finite difference method, finite element method, Galerkin method, etc.

Table of Contents

1.Introduction. 2. Multiresolution Analysis. 3. Approximation in Multiscale Basis. 4. Multiscale Solution of Weakly Singular IntegralEquations of Second Kind with Abel type and Logarithmic Kernels. 5. Multiscale Solution of Cauchy Singular Integral Equations ofSecond Kind. 6. Multiscale Solution of Hypersingular Integral Equations of Second Kind. 7. Multiscale Solution of Nonlinear SingularIntegral/Integro-differential Equations.

About the Authors

Professor Panja is an Associate Professor in the Department of Mathematics at Visva Bharati in Santiniketan, India. He earned his BSc(Hons) in Mathematics from the University of Calcutta in 1983 and his MSc in Applied Mathematics in 1986. In 1993 he obtained his PhD in Mathematical Physics from Visva Bharati. He has published eight articles in the past three years.

Professor Birendra Nath Mandal is a retired Professor of Physics and Applied Mathematics Unit at the Indian Statistical Institute in Kolkata. He obtained his BSc(Hons) in Mathematics, Physics, Chemistry in 1964, his MSc in Applied Mathematics with Geodesy Geophysics as a specialty paper in 1966, and his PhD in Continuum Mechanics in 1973 from Calcutta University. He has been awarded the McCan Silver Medal (1964), University Gold Medal and Prize (1966), Hemchandra Gossain Gold Medal and Prize (1966), Debendranath Gangopadhyay Gold Medal (1966), Chirendra Chandra Deb Memorial Silver Medal (1966), Lokmanya Bal Gangadhar Tilak Memorial Silver Medal and Prize (1966), Commonwealth Fellowship for post doctorate research in the UK (1973-75), INSA Royal Society Exchange Visitor, Bristol University, UK (June-July 1998), and NASI Platinum Jubilee Senior Scientist (2009 - 2014). Professor Mandal specializes in the following research fields: integral equations, integral transforms, wavelets, optimization via genetic algorithm, fluid mechanics (water waves), elasticity, wave propagation problems in continuous media, inventory models, and queuing models.

Subject Categories

BISAC Subject Codes/Headings:
MAT007000
MATHEMATICS / Differential Equations
MAT021000
MATHEMATICS / Number Systems
MAT037000
MATHEMATICS / Functional Analysis
SCI086000
SCIENCE / Life Sciences / General