Computational Methods for Integral Equations: Linear Legendre Multi-Wavelets and Homotopy Analysis Methods

Due to the ability of function representation, hybrid functions and wavelets have a special position in research. In this book, we state elementary definitions, then we introduce hybrid functions and some wavelets such as Haar, Daubechies, Chebyshev, sine-cosine and linear Legendre multi wavelets (LLMW). We use LLMW method to find the numerical solution of some kind of integral equations. The main advantage of the wavelet technique for solving a problem is its ability to transform complex problems into a system of algebraic equations. We apply this property to several kind of integral equations. Homotopy Analysis Method (HAM) is the second Method which has been used for solving integral equations. HAM is an analytic technique to solve the linear and nonlinear equations which can be used to obtain the numerical solution too. We extend the application of homotopy analysis method for solving linear integro-differential equations and Fredholm and Volterra integral equations. This book also included a new representations of wavelets base on floor function which can be attractive in computational point of view.