| This thesis mainly studies that we use an improved post-processing method to solve the second-kind Fredholm integral equations and eigen-problems with compact integral operator. This method combines projection and post-processing technology to improve the convergence order of approximate solutions. In the first place, it solve the equation using projection method to obtain the primary approximate solution un. In the second place, we use post-processing techniques acting the primary approximate solution in order to get the results we need. Finally, the approximation convergence band from O(hr+1) up to O(h2r+2), through the post-processing method solve integral equation and eigen-problems. Full text is divided into three chapters:The chapter 2, we discuss that using projection post-processing method to solve the second-kind Fredholm integral equations. Firstly, we study the theoret-ical framework of projection post-processing method and analyse the error. Then we introduce Galerkin post-processing algorithm and collocation post-processing algorithm to solve the second kind of integral equations. We use traditional pro-jection scheme to solve the second-kind Fredholm integral equations. Then we get higher convergence order for the integral equations by using the interpolation post-processing technique which restructuring the high order basis function ψ.The chapter 3, we mainly engaged in structure the multiscale wavelet and wavelet space. At the same time, we use it resolve compact integral operator eigen-problems as basis functions. When using the projector post-processing algorithm, we resolve eigen-problems combining it with multi-scale wavelets. In this chapter, we apply multiscale Galerkin post-processing to resolve eigenvalue problem which increase the convergence order of approximate solution from O(hr+1) to O(h2r+2). According to the characteristics of coefficient matrix An, we propose a compression algorithms to speed up the calculation at the same time. |
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