| The integral equation is an important tool of describing physical problem. There are many problems in the field of eletrostatics, dynamoelectic, elasticity mechanics, hydrodynamics, geophysical and the theory of electromagnetic and radicalizations which can be changed into the problems of integral equation. Definite problem of ODE and PDE can also be changed into the equivalence integral problem. The numerical method of solving PDE inverse problem often leads into the first kind Fredholm equation.The second kind Fredholm integral equation is the linear inhomogeneous integral equation. Its theory is very classical. It plays a very important role in the development of the functional analysis theory.This paper uses Galerkin method to solve second kind Fredholm integral equations. Daubechies compactly supported orthonormal wavelets has been applied. The skill of Y.Meyer interval wavelets is employed. A new method is introduced. This method can improve precision greatly and at the same time use less computation in some situation. The error can limit below 10-10. Numerical examples are provided and approve the method be in effect.The first chapter of the paper introduces the theory of the second kind linear integral equation, including the existence and uniqueness of the equation, the solving method of some special function, the enumerical computation of the function and the estimation of error.The second chapter introduces the theory of wavelet analysis. It first presents the concept of the wavelet and wavelet transform, then the concept of MRA and Mallat algorithm. In the last two parts of the chapter, it introduces the theory of compact supported wavelets and interval wavelets.The third chapter of the paper is the main chapter of the masteral dissertation. It first introduces the general algorithm, and then estimates the error, in the last, it gives three enumerical examples and proves the method be effective. |
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