ABSTRACT
This chapter involves the numerical techniques based on wavelets for solving the Volterra integro-differential equations system. Integral equations occur naturally in many fields of science and engineering [208]. Wavelets theory is a relatively new and emerging area in the field of applied science and engineering. It has been applied in a wide range of engineering disciplines; particularly, wavelets are very successfully used in signal analysis for waveform representations and segmentations, time frequency analysis, and fast algorithms for easy implementation [54]. Wavelets permit the accurate representation of a variety of functions and operators. Moreover wavelets establish a connection with fast numerical algorithms [32]. Wavelets are powerful tools to explore a new direction in solving differential equations and integral equations. In recent years, approximation based on basis functions has been used to estimate the solutions of integral equations, such as orthogonal functions and wavelets. Generally, the sets of piece-wise constant orthogonal functions (e.g., Walsh, Block-Pulse, Haar, etc.), the sets of orthogonal polynomials (e.g., Laguerre, Legendre, Chebyshev, etc.) and the sets of sine-cosine functions in Fourier series have been applied to solve integral equations. One of the most attractive
solution of integral equations. The wavelets technique allows the creation of very fast algorithms when compared to the algorithms ordinarily used.
