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Wavelets Based Collocation Method for Two Types of Integral Equations and Estimation of Error Bound

Author: YinYi
Tutor: YuHaiYuan
School: Xiangtan University
Course: Computational Mathematics
Keywords: Haar wavelet FSAI algorithm Wavelet multigrid method Integral equation Collocation method
CLC: O241.82
Type: Master's thesis
Year: 2008
Downloads: 54
Quote: 0
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Abstract


Since the introduction of the concept of multi - resolution analysis , wavelet analysis and its application has been booming , involved were broad , far-reaching effects , rapid development is unprecedented . The wavelet advantage essentially stems from both smooth and locally compact nature of the support , enabling better than the traditional method of processing local singularity problem in this article through the use of multi-resolution similarity between the analysis and multigrid methods , numerical methods of solving symmetric -FSAI method by numerical experiments to verify the feasibility of wavelet coefficients of the linear equations for the first class of Volterra integral equations using Haar wavelet collocation method theoretically rigorous proof of the convergence of the method , the values the gradual progress of solutions and precision extrapolation formula , and gives the results of numerical experiments show that the correctness of the theoretical analysis results , and for the first Fredholm integral equation , a numerical example illustrates the limitations of the method , itemized gradually progress style reveals the method used to solve the Fredholm integral equation convergence mechanism , and finally using wavelet multigrid method for solving the discrete system and given a fast algorithm to calculate the format .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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