Wavelet analysis: the scalable structure of information
Wavelet analysis: the scalable structure of information
Wavelet-Galerkin method for integro-differential equations
Applied Numerical Mathematics
Solving second kind integral equations by Galerkin methods with continuous orthogonal wavelets
Journal of Computational and Applied Mathematics
An Implementation of Fast Wavelet Galerkin Methods for Integral Equations of the Second Kind
Journal of Scientific Computing
Fast solvers of integral equations of the second kind: wavelet methods
Journal of Complexity
A fast numerical solution method for two dimensional Fredholm integral equations of the second kind
Applied Numerical Mathematics
Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations
Mathematics and Computers in Simulation
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In this paper, we apply the wavelet-Galerkin method to obtain approximate solutions to linear Volterra integral equations (VIEs) of the second kind. Daubechies wavelets are used to find such approximations. In this approach, we introduce some new connection coefficients and discuss their properties and propose algorithms to evaluate them. These coefficients can be computed just once and applied for solving every linear VIE of the second kind. Convergence and error analysis are discussed and numerical examples illustrate the efficiency of the method.