Approxmiation Of Daubechies Wavelet Function With Legendre Orthogonal Polynomials And Finite Element Method

This paper mainly discussed the problem of approximation Daubechies wavelets with Legendre orthogonal polynomials , then by the obtained results, we analysis the problem of rectangular thin plate small deflection. Firstly, we calculate many process variables w_j^k+1(j,k = 0,1.…) and the coefficient a_n(n = 0,1,…) of Legendre polynomials.then we get approximation expressionφ|^x and figure of Legendre polynomials approximation scale functionφ(x) ,and we get approximation expressionΨ|^x and figure of Legendre polynomials approximation wavelet functionΨ(x) by two scale relation. Further we use the results approximation two dimensional tensor form Daubechies wavelet function and scale function, thus we get their images of approximation scale function and approximation wavelet function. moreover, we also obtained their images of first and second order partial derivative. Secondly, we use the results of approximation two dimensional tensor form Daubechies wavelet function analysis the problem of rectangular thin plate small deflection, and get approximation solution, farther analyze that boundary problem. Finally, we get estimation approximation order is O(h⁴).