Wavelet Based Approximation Schemes for Singular Integral Equations - Panja, Madan Mohan
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Présentation Wavelet Based Approximation Schemes For Singular Integral Equations Format Broché
- Livre
Résumé :
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.
Sommaire: 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