The Study Of Quasi Wavelet Based Numerical Method Applied To A Class Of Partial Integro-Differential Equation

The integro-differential equation of parabolic type often occurs in ap-plications such as heat conduction in material with memory, compression of poro-viscoelastic media, population dynamics, nuclear reactor dynamics, etc .There are lots of documents of V.Thomee [14,16,19,21,24,28,29], Stig. Larsson[21], W. Mclean[16,24,28],C.Lubich[25], J.C.Lopeez-marcos [15], J. M.Sanz-Serna[12], G Fairweather[19,20], L. Wahlbin[14,28,21], I. H.Sloan[25,29] in overseas and Chen Chuanmiao [14], Yun-qing Huang [30], Da Xu [18,42,43,44], Tao Tang[26], Qiya Hu [30]in home. A lot of them use FEM;Spline collocation methods; finite difference methods; Spectral colloca-tion methods. But few of them make the global behavior of fully discrete by wavelet method.Based on Mallat multiresolution analysis, arbitrary wavelet subspace can be standardized by a group of orthogonal wavelet generation, this group of wavelet-base can be regularized by its own corresponding combination of or-thogonal scaling function to be normalized. However, standardization of the general orthogonal scaling function of the Fourier transform is not continu-ous, so there is no good standardized orthogonal local features, which is not conductive to numerical calculation. In order to improve standardization of orthogonal scaling function and gradual localization of features, we have its regular treatment. This is the main idea of quasi-wavelet algorithm. To test the quasi-wavelet algorithm and the boundary treatment of the validity and accuracy, This article uses the quasi-wavelet algorithm for a class of partial integro-differential equation to the numerical solution of quasi wavelet.The Euler method numerical discrete scheme is used to discrete the space and the quasi-wavelet method is used to discrete time.Main results follows:(1)Given the main introduction about wavelet and quasi-wavelet method.(2)Given the discrete scheme of a class of integro-differential equation and the numerical experiments result. (3) Shown the importance of regularization by comparing and given the result graphics.(4)Given the future plan about the research.