Wavelets Based Collocation Method For Two Types Of Integral Equations And Estimation Of Error Bound

Wavelet analysis and its application made a great progress since the conception of multiresolution analysis came out.It has spread to extensive fields and made great difference.Essentially,the advantage of wavelets root in its smoothness and locally compactly supported property,thereby it is more suitable to deal with problems with local singularity than usual methods.In this paper,a new numerical method-FSAI Method is introduced to solve the asymmetrical problems by the comparison between the multiresolution analysis and multigrid method.Its availability is checked by some numerical tests.For Volterra integral equation of first kind,we apply Haar wavelet collocation method to obtain the linear equations system of wavelet coefficients,meanwhile, its convergence is proven by theory,and the asymptotic extensions of numerical solution is obtained as well as the high-accuracy extrapolation formula.In addition, the results of corresponding numerical tests are given,which conforms the correctness theory analysis.For Fredholm integral equations of first kind,we demonstrate the limitation of this method by a numerical test,and we show the convergence of this method in solve Fredholm integral equations of first kind by term asymptotic expansions.Besides for Fredholm integral equations of first kind,we use Haar wavelets collocation method to get the linear equations system of wavelet coefficients and solve it by wavelet multigrid method.At last a corresponding fast algorithm is introduced.