Numerical Solution Of Fredholm Type Integral Equation By Using Wavelets

Many scientific and engineering problems of the mathematic can be attributed to the solution of integral or differential equations.Along with the 20th century,the rapid development of science and technology,making the demand of equations increasing highly,especially the accurately numerical solution.High-precision numerical solution for the practical problems have a significant impact,arising from the variety of numerical solutions.Although wavelet methods developed the relatively late,it was the most rapid.Because of many good approximations,wavelets method was widely used in various areas.This paper research the applications of wavelets method in solving Fredholm integral equations and integral - differential equations,some results are obtained.The paper is organized as follows:In Chapter 1,The basic knowledge of wavelets analysis and integral equation is introduced.We discuss the relationship between wavelets and integral equations,illustrating essential of using wavelets method.In Chapter 2,we study several numerical methods of integral equations,the comparative analysis of these methods shows that the key to the application of wavelets.In Chapter 3,discussion of wavelets Galerkin method,integral wavelets operator matrix are given.Numerical solution of Fredholm type integral equation by using wavelets is studied.Illustrating examples are included to demonstrate the validity and applicability of the technique.