Wavelet Finite Element Method For Two Types Of Nonlinear Parabolic Equations

Nonlinear parabolic equation is a class of evolution equations, and its initial boundary value problem in science and engineering has a wide range of applications, often used to describe heat conduction, molecular diffusion, flow in porous media such as the law changes over time and Process, but solving large numerical calculation of these issues. Wavelet finite element method based on wavelet functions, with algorithm stability, high operation speed, high precision calculations, so the numerical solution of partial differential equations and deal with local stress concentration such singularity has attractive advantages.The paper based on the basic theory of wavelet finite element, choose B-spline wavelet on the interval, systematically studies wavelet finite element method for wavelet finite element method of second order nonlinear parabolic equations and third-order nonlinear parabolic equations.Firstly, gives a brief history and commentary on the wavelet finite element method, but also illustrates the thesis of practical value, then introduces the basic theories of wavelet finite element knowledge, important inequalities and B-spline wavelet on the interval functions and scaling functions. In order to wavelet finite element method is applied to nonlinear parabolic equations in numerical solution of the theoretical foundation.Secondly, the B-spline wavelet on the interval finite element method of approximating the numerical solution of second-order nonlinear parabolic, Burgers-Fisher equation and RLW equation is presented. Convergence analysis is given. Numerical examples show the advantages of the method.In the end, the B-spline wavelet on the interval finite element scheme of three-order nonlinear parabolic equations, Korteweg-de Vries equation is constructed. In order to show the efficiency of the presented method, a problem is considered. And the numerical simulation of the problem in the different times is done.