Wavelet Numerical Method For Two Types Of Partial Differential Equations

Along with the rapid development of science and technology, for many scientific andengineering problems of equations solution especially precision demand of numericalsolution is higher and higher. Wavelet numerical method for solving the numerical methodis developed in recent years. Due to wavelet has smoothness and local compactly,compared with the traditional method for solving partial differential equations. Thewavelet can better solve the problem of singularity, so its development speed is veryfast.Recent years, wavelet which has many good natures applied in the numerical solutionof partial differential equations has been greatly concerned to. The organization of thepaper takes three parts as follows:First of all, the thesis introduces the development and application status of waveletanalysisthe partial differential equation and. Then, introducing the related definition andproperties of the wavelet.In order to wavelet finite element method is applied to the partialdifferential equations in numerical solution of the theoretical foundation.Secondly, Made a study of the Haar wavelet and its integral matrix, researched intothe Haar integral method of a class of partial differential equations.Finally, the thesis studies the Shannon wavelet numerical solution of the equationsbased on Hopf-Cole transform of Burgers equation. By using wavelet analysis theory forthe Burgers equation, the one-dimensional Shannon scaling function was introduced tosolve the partial differential equations. Firstly, the Burgers equation transform into thelinear diffusion equation by using Hopf-Cole transform. Chosen the interpolation featuresand the each order derivative of Shannon scale function, and using the wavelet collocationmethod for a class of linear space discrete diffusion equation. It is obtained the differentialequations with time, then the Runge-Kutta method for solving the equations.