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 in applied science and engineering.
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 in applied science and engineering.
M M Panja has a MSc in Applied Mathematics (1987) from Calcutta University, India, and a PhD (1993) from Visva-Bharati University, India. He investigated the origin of (hidden) geometric phase on quantum mechanical problems and initiated studies on Lie group theoretic approach of differential equations during his postdoctoral research. His investigations (2007) on approximation theory based on multiresolution analysis, has been published several international journals. His current research interests are (i) multiscale approximation based on wavelets, and (ii) similarity (exact) solution of mathematical models involving differential and integral operators. B N Mandal has a MSc in Applied Mathematics (1966) and a PhD (1973) from Calcutta University, India. He was a postdoctoral Commonwealth Fellow at Manchester University, 1973-75. He was faculty at Calcutta University, 1970-89 and later at Indian Statistical Institute (ISI), Kolkata, 1989-2005. He was a NASI Senior Scientist, 2009-14 in ISI. His research work encompasses several areas of applied mathematics including water waves, integral transforms, integral equations, inventory problems, wavelets etc. He has published a number of works with reputable publishers. He has supervised PhD theses of more than 20 candidates and has more than 275 research publications.
Inhaltsangabe
Introduction Singular integral equation MRA of Function Spaces Multiresolution analysis of L2(R) Multiresolution analysis of L2([a, b] ¿ R) Others Approximations in Multiscale Basis Multiscale approximation of functions Sparse approximation of functions in higher dimensions Moments Quadrature rules Multiscale representation of differential operators Representation of the derivative of a function in LMW basis Multiscale representation of integral operators Estimates of local Holder indices Error estimates in the multiscale approximation Nonlinear/Best n-term approximation Weakly Singular Kernels Existence and uniqueness Logarithmic singular kernel Kernels with algebraic singularity An Integral Equation with Fixed Singularity Method based on scale functions in Daubechies family Cauchy Singular Kernels Prerequisites Basis comprising truncated scale functions in Daubechies family Multiwavelet family Hypersingular Kernels Finite part integrals involving hypersingular functions Existing methods Reduction to Cauchy singular integro-differential equation Method based on LMW basis
Introduction Singular integral equation MRA of Function Spaces Multiresolution analysis of L2(R) Multiresolution analysis of L2([a, b] ¿ R) Others Approximations in Multiscale Basis Multiscale approximation of functions Sparse approximation of functions in higher dimensions Moments Quadrature rules Multiscale representation of differential operators Representation of the derivative of a function in LMW basis Multiscale representation of integral operators Estimates of local Holder indices Error estimates in the multiscale approximation Nonlinear/Best n-term approximation Weakly Singular Kernels Existence and uniqueness Logarithmic singular kernel Kernels with algebraic singularity An Integral Equation with Fixed Singularity Method based on scale functions in Daubechies family Cauchy Singular Kernels Prerequisites Basis comprising truncated scale functions in Daubechies family Multiwavelet family Hypersingular Kernels Finite part integrals involving hypersingular functions Existing methods Reduction to Cauchy singular integro-differential equation Method based on LMW basis
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