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.
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.