Numerical solutions of integral equations by using CAS wavelets

Abstract

Wavelets are mathematical functions that cut up data into different frequency components and study each component with a resolution matched to its scale. They have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. Wavelets are developed independently in the field of mathematics, quantum physics, electrical engineering, and seismic geology. Interchange between this field during the last ten years have led to many new wavelet application such as image compression, turbulence, human vision, radar and earthquake prediction. In this we introduce a numerical method of solving integral equation by using CAS wavelets. This method is method upon CAS wavelet approximations. The properties of CAS wavelets are first presented. CAS wavelet approximations methods are then utilized to reduce the integral equations to the solution of algebraic equations.