The Wavelat Method For Solving Singular Intergral And Singular Intergral Equations With Hilbert Kernel

This paper first presents some speculative knowledge of the wavelet analysis,such asMutli-Resolution Analysis, Wavelet Transform,Triangle Hermite interpolation waveletoperator, and then together Triangle Hermite interpolation wavelet operator and being thekernel into triangular infinite series, derived a category of relatively simple formula, andgives examples to test our quadrature formula has relatively high accuracyFinally,We introduced the theory of singular integral equations, According to the appropriateconditions of triangular Hermite interpolation wavelet operator,the Hilbert singular integral equations arediscretized into linear equations, Get the coefficient matrix is antisymmetric, and the fourth blockof the matrix is zero matrix, for an order of 2ⁿ⁺²Ã—2ⁿ⁺² coefficient matrix, we need tocalculate the number of elements is much less than half of the total matrix elements, greatlyreducing the amount of computation. In addition, a numerical example is the validity of theresults.