Numerical Solution of Integral Equations by using Discrete GHM Multi-wavelet
In this paper, numerical solution based on discrete GHM multi-wavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete Geronimo-Hardin-Massopust (GHM) multi-wavelet. The localization property, robustness and other features of wavelets are essential for solving integral equations efficiently. A number of examples are demonstrated to justify the applicability of the method. In GHM multi-wavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient when compared to Quadrature method.
GHM Multi-wavelet, Fredholm integral equations, Quadrature Method, Function Approximation, Scaling.